Chapter 1 In Class Review Name______________________________________

1. The data below represents the resting heart rates for a random sample of males and females in AP Stats.

Females: 47 60 61 65 65 69 70 70 70 70 70 70
72 72 72 73 75 75 76 78 80 82 83 90

Males: 60 60 60 60 61 61 64 64 64 66 66 66
70 70 70 70 72 73 79 84 90 90 94 112

Make back-to-back stemplots of the data. Make sure you include a key. Then compare the distributions.
2. The data below represents the number of contacts for a sample of 20 female AP Stats students.

66 100 114 140 143 148 177 197 226 241 249 279 293

318 354 385 429 528 1104 2168

a. Calculate the following summary statistics. Round to the nearest tenth, if necessary.

5 Number Summary
n 𝑥𝑥̅ 𝑠𝑠𝑥𝑥 Min Q1 Med Q3 Max IQR
Female

b. Determine if there are any outliers for either data set. Show calculations to justify your answer.

c. Sketch a boxplot of the distribution. Then describe the distribution.

3. The scores on a statistics test had a mean of 81 and a standard deviation of 9. One student was absent on the
test day, and his score wasn’t included in the calculation. If his score of 84 was added to the distribution of
scores, what would happen to the mean and standard deviation?
(a) Mean will increase, and standard deviation will increase.
(b) Mean will increase, and standard deviation will decrease.
(c) Mean will increase, and standard deviation will stay the same.
(d) Mean will decrease, and standard deviation will increase.
(e) Mean will decrease, and standard deviation will decrease.

4. You look at real estate ads for houses in Naples, Florida. There are many houses ranging from $200,000 to
$500,000 in price. The few houses on the water, however, have prices up to $15 million. The distribution of
house prices will be
(a) skewed to the left.
(b) roughly symmetric.
(c) skewed to the right.
(d) unimodal.
(e) too high.

5. When comparing two distributions, it would be best to use relative frequency histograms rather than frequency
histograms when
(a) the distributions have different shapes.
(b) the distributions have different spreads.
(c) the distributions have different centers.
(d) the distributions have different numbers of observations.
(e) at least one of the distributions has outliers.

6. If a distribution is skewed to the right with no outliers,

(a) mean < median.
(b) mean ≈ median.
(c) mean = median.
(d) mean > median.
(e) We can’t tell without examining the data.

7. A sample of 269 people were asked “What flavor of ice cream would you pick?” Below is a two-way table of
responses to this question and age. Which of the following conclusions seems to be supported by the data?

(a) There is no association between ice cream flavor preference and age.
(b) The proportion of children that chose chocolate was higher than the proportion of adults that chose
chocolate.
(c) The proportion of teens that chose vanilla was higher than the proportion of children that chose vanilla.
(d) Adults like ice cream more than children and teens.
(e) The marginal distribution of ice cream flavor is 77, 73, 119.
8. The mean and median selling prices of existing single-family homes sold in July 2012 were $263,200 and
$224,200. Which of these numbers is the mean and which is the median? Explain how you know.

9. If a distribution is skewed, which measure of center and spread should be used to describe the distribution?

10. Do male doctors perform more cesarean sections (C-sections) than female doctors? A study in Switzerland
examined the number of cesarean sections (surgical deliveries of babies) performed in a year by samples of male
and female doctors. Here are summary statistics for the two distributions:

(a) Based on the computer output, which distribution would you guess has a more symmetrical shape? Explain.

(b) Explain how the IQRs of these two distributions can be so similar even though the standard deviations are
quite different.

(c) Determine if there are any outliers in each distribution. Show work.
(e) A distribution of test scores is approximately Normal and Joe scores at the 85th percentile. How
many standard deviations above the mean did he score?

(f) In a Normal distribution, Q1 is how many SD below the mean?

Alternate Example: Serving Speed

In the 2008 Wimbledon tennis tournament, Rafael Nadal averaged 115 miles per hour (mph) on his first
serves. Assume that the distribution of his first serve speeds is Normal with a mean of 115 mph and a
standard deviation of 6 mph.

(a) About what proportion of his first serves would you expect to be slower than 103 mph?

(b) About what proportion of his first serves would you expect to exceed 120 mph?

(c) What percent of Rafael Nadal’s first serves are between 100 and 110 mph?

(d) The fastest 30% of Nadal’s first serves go at least what speed?

(e) A different player has a standard deviation of 8 mph on his first serves and 20% of his serves go less
than 100 mph. If the distribution of his serve speeds is approximately Normal, what is his average first
serve speed?

17
2.2 Normal Calculations Practice

1. Suppose that Clayton Kershaw of the Los Angeles Dodgers throws his fastball with a mean velocity
of 94 miles per hour (mph) and a standard deviation of 2 mph and that the distribution of his fastball
speeds can be modeled by a Normal distribution.

(a) Make an accurate sketch of the fastball distribution with the horizontal axis marked in mph.

(b) Use the 68-95-99.7 rule to find the proportion of fastballs that will travel at least 100 mph.

(c) Use the 68-95-99.7 rule to find the proportion of fastballs that will travel between 92 and 98
mph.

(d) Find the proportion of fastballs that will travel between 93 and 95 mph.

(e) Find the proportion of fastballs that will travel at least 97 mph.

(f) What is the 25th percentile of Kershaw’s distribution of fastball velocities?

(g) What fastball velocities would be considered low outliers for Kershaw?

18
Chapter 3 Review

Exercises 1-5 refer to the following setting.

Measurements on young children in Mumbai, India, found this least-squares line for predicting height y from arm span x:

𝑦𝑦� = 6.4 + 0.93𝑥𝑥

Measurements are in centimeters (cm).

1. By looking at the equation of the least-squares regression line, you can see that the correlation between height
and arm span is

(a) greater than zero.

(b) less than zero.
(c) 0.93.
(d) 6.4.
(e) Can’t tell without seeing the data.

2. In addition to the regression line, the report on the Mumbai measurements says that r2 = 0.95. This suggests
that

(a) although arm span and height are correlated, arm span does not predict height very accurately.
(b) height increases by .97 cm for each additional centimeter of arm span.
(c) 95% of the relationship between height and arm span is accounted for by the regression line.
(d) 95% of the variation in height is accounted for by the regression line.
(e) 95% of the height measurements are accounted for by the regression line.

3. One child in the Mumbai study had height 59 cm and arm span 60 cm. This child’s residual is

(a) −3.2 cm.

(b) −2.2 cm.
(c) −1.3 cm.
(d) 3.2 cm.
(e) 62.2 cm.

4. Suppose that a tall child with arm span 120 cm and height 118 cm was added to the sample used in this study.
What effect will adding this child have on the correlation and the slope of the least-squares regression line?
(a) Correlation will increase, slope will increase.
(b) Correlation will increase, slope will stay the same.
(c) Correlation will increase, slope will decrease.
(d) Correlation will stay the same, slope will stay the same.
(e) Correlation will stay the same, slope will increase.

5. Suppose that the measurements of arm span and height were converted from centimeters to meters by dividing
each measurement by 100. How will this conversion affect the values of r2 and s?

(a) r2 will increase, s will increase.

(b) r2 will increase, s will stay the same.
(c) r2 will increase, s will decrease.
(d) r2 will stay the same, s will stay the same.
(e) r2 will stay the same, s will decrease.

24
6. You have data for many years on the average price of a barrel of oil and the average retail price of a gallon of
unleaded regular gasoline. If you want to see how well the price of oil predicts the price of gas, then you should
make a scatterplot with _______ as the explanatory variable.

(a) the price of oil

(b) the price of gas
(c) the year
(d) either oil price or gas price
(e) time

7. In a scatterplot of the average price of a barrel of oil and the average retail price of a gallon of gas, you expect to
see

(a) very little association.

(b) a weak negative association.
(c) a strong negative association.
(d) a weak positive association.
(e) a strong positive association.

8. If women always married men who were 2 years older than themselves, what would the correlation between
the ages of husband and wife be?

(a) 2
(b) 1
(c) 0.5
(d) 0
(e) Can’t tell without seeing the data

9. Which of the following is not a characteristic of the least-squares regression line?

(a) The slope of the least-squares regression line is always between −1 and 1.
(b) The least-squares regression line always goes through the point ( x , y ).
(c) The least-squares regression line minimizes the sum of squared residuals.
(d) The slope of the least-squares regression line will always have the same sign as the correlation.
(e) The least-squares regression line is not resistant to outliers.

10. The figure to the right is a scatterplot of reading test scores against IQ test scores for 14 fifth-grade children.
There is one low outlier in the plot. What effect does this low outlier have on the correlation?

(a) It makes the correlation closer to 1.

(b) It makes the correlation closer to 0 but still positive.
(c) It makes the correlation equal to 0.
(d) It makes the correlation negative.
(e) It has no effect on the correlation.

25
11. The manager of a grocery store selected a random sample of 11 customers to investigate the relationship
between the number of customers in a checkout line and the time to finish checkout. As soon as the selected
customer entered the end of the checkout line, data were collected on the number of customers in line who
were in front of the selected customer and the time, in seconds until the selected customer was finished with
the checkout. The data are shown in the following scatterplot along with the corresponding LSRL and computer
output.

a. Describe what the scatterplot reveals about the relationship between number of customers in line and the
time it takes to checkout.

b. What is the equation of the LSRL?

c. Identify and interpret in context the estimate of the slope for the LSRL.

d. Identify and interpret in context the estimate of the intercept for the LSRL.

e. Calculate and interpret the residual for a customer who was in a line with 3 people and finished checking out
after 200 seconds.

26
 f. Identify and interpret the standard deviation of the residuals in context.

g. Identify and interpret in context the coefficient of determination, r2.

h. One of the data points was determined to be an outlier. Circle the point on the scatterplot and explain why
it is considered an outlier. If this point were removed from the plot, what effect would it have on the
correlation?

12. Each year, students in an elementary school take a standardized math test at the end of the school year. For a
class of fourth-graders, the average score was 55.1 with a standard deviation of 12.3. In the third grade, these
same students had an average score of 61.7 with a standard deviation of 14.0. The correlation between the two
sets of scores is r = 0.95. Calculate the equation of the least-squares regression line for predicting a fourth-grade
score from a third-grade score.

27
 AP STATISTICS Test Booklet

Chapter 4 Review

1. A well-designed experiment should have which of the following characteristics?

I. Subjects assigned randomly to treatments

II. A control group or at least two treatment groups

III. Replication
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III

2. A florist wanted to investigate whether a new powder added to the water of cut flowers helps to keep the flowers
fresh longer than just water alone. For a shipment of roses that was delivered to the store, the florist flipped a coin
before placing each rose in its own individual container with water. If the coin landed heads up, the rose was placed
in water with the new powder; otherwise, the rose was placed in water alone. Which of the following is the best
description of the method used by the florist?
(A) A census, because all roses are assigned to a container
(B) An experiment with a completely randomized design
(C) An experiment with a blocked design, with blocking by type of water
(D) An experiment with a matched-pairs design
(E) An observational study

3. Researchers conducted a study to investigate the effects of soft drink consumption on fat stored in muscle tissue.
From a sample of 80 adult volunteers, 40 were randomly assigned to consume one liter of a soft drink each day. The
remaining 40 were asked to drink one liter of water each day and not to consume any soft drinks. At the end of six
months, the amount of fat stored in each person’s muscle tissue was recorded. The people in the group who drank
the soft drink had, on average, a higher percentage of fat stored in the tissue than the people who drank only water.
Which of the following is the most appropriate conclusion?
There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only
(A)
water, and the conclusion can be generalized to all adults.
There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only
(B)
water, and the conclusion can be generalized to all people who consume soft drinks.
There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only
(C)
water, and the conclusion can be generalized to adults similar to those in the study.
Although cause-and-effect cannot be established, there is an association between consuming soft drinks and
(D)
fat storage in muscle tissue for the population of all adults.
Although cause-and-effect cannot be established, there is an association between consuming soft drinks and
(E)
fat storage in muscle tissue for the population of all adults who consume soft drinks.

AP Statistics Page 1 of 6
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Chapter 4 Review

4. A compact disc (CD) manufacturer wanted to determine which of two different cover designs for a newly released
CD will generate more sales. The manufacturer chose 70 stores to sell the CD. Thirty-five of these stores were
randomly assigned to sell CDs with one of the cover designs and the other 35 were assigned to sell the CDs with the
other cover design. The manufacturer recorded the number of CDs sold at each of the stores and found a significant
difference between the mean number of CDs sold for the two cover designs. Which of the following gives the
conclusion that should be made based on the results and provides the best explanation for the conclusion?
It is not reasonable to conclude that the difference in sales was caused by the different cover designs because
(A)
this was not an experiment.
It is not reasonable to conclude that the difference in sales was caused by the different cover designs because
(B)
there was no control group for comparison.
It is not reasonable to conclude that the difference in sales was caused by the different cover designs because
(C)
the 70 stores were not randomly chosen.
It is reasonable to conclude that the difference in sales was caused by the different cover designs because the
(D)
cover designs were randomly assigned to stores.
It is reasonable to conclude that the difference in sales was caused by the different cover designs because the
(E)
sample size was large.

5. Which of the following can be used to show a cause-and-effect relationship between two variables?
(A) A census
(B) A controlled experiment
(C) An observational study
(D) A sample survey
(E) A cross-sectional survey

6. Which of the following distinguishes an observational study from a randomized experiment?

In an observational study volunteers are always used, whereas in a randomized experiment a random sample
(A)
is always taken from the population.
In an observational study a random sample is always taken from the population, whereas in a randomized
(B)
experiment volunteers are always used.
In an observational study treatments are not randomly assigned, whereas in a randomized experiment
(C)
treatments are randomly assigned.
In an observational study a control group is never used, whereas in a randomized experiment a control group
(D)
is always used.
An observational study can be double-blind, whereas a randomized experiment can only be single-blind
(E)
because the experimenter determines who is randomly assigned to each treatment.

7. Under which of the following conditions is it preferable to use stratified random sampling rather than simple
random sampling?

Page 2 of 6 AP Statistics
 Test Booklet

Chapter 4 Review

The population can be divided into a large number of strata so that each stratum contains only a few
(A)
individuals.
The population can be divided into a small number of strata so that each stratum contains a large number of
(B)
individuals.
(C) The population can be divided into strata so that the individuals in each stratum are as much alike as possible.
(D) The population can be divided into strata so that the individuals in each stratum are as different as possible.
The population can be divided into strata of equal sizes so that each individual in the population still has the
(E)
same chance of being selected.

8. A large simple random sample of people aged nineteen to thirty living in the state of Colorado was surveyed to
determine which of two MP3 players just developed by a new company was preferred. To which of the following
populations can the results of this survey be safely generalized?
(A) Only people aged nineteen to thirty living in the state of Colorado who were in this survey
(B) Only people aged nineteen to thirty living in the state of Colorado
(C) All people living in the state of Colorado
(D) Only people aged nineteen to thirty living in the United States
(E) All people living in the United States

9. Some contact lens wearers report problems with dryness in their eyes. A study was conducted to evaluate the
effectiveness of a new eye-drop solution to relieve dryness for contact lens wearers. Twenty-five volunteers who
wore contact lenses agreed to use the new solution for one month. At the end of the month, 36 percent of the
volunteers reported that the new solution was effective in relieving dryness. The company that produced the new
eye-drop solution concluded that using the new solution is more effective in relieving dryness than using no
solution. Which of the following best explains why the study does not support such a conclusion?
(A) The sample size was too small.
(B) The study had no control group.
(C) The participants were volunteers.
(D) The participants self-reported the frequency with which they used the new solution.
(E) The participants self-reported the effectiveness of the new solution.

10. Mr. Ikeler conducted a study investigating the effectiveness of a new method for teaching a mathematics unit. He
recruited 80 students at a college and randomly assigned them to two groups. Group 1 was taught with the new
method, and group 2 was taught with the traditional method. Both groups were taught by the same teacher. At the
end of the unit, an achievement test was administered and used to make a comparison of the two groups. What is the
response variable in the study?
(A) The new teaching method
(B) The traditional teaching method
(C) The teacher in the study
(D) The score on the achievement test
(E) The 80 students

AP Statistics Page 3 of 6
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Chapter 4 Review

11. A researcher selects a simple random sample of 1,200 women who are students at Midwestern colleges in the
United States to use for an observational study. Which of the following describes the population to which it would
be most reasonable to generalize the results?
(A) All students in the United States
(B) All college students in the United States
(C) All women who are students in the United States
(D) All students at Midwestern colleges in the United States
(E) All women who are students at Midwestern colleges in the United States

12. An experiment was designed to investigate the relationship between the dosage of a certain migraine medication
and the amount of time until relief from the headache was experienced. Four dosages in milligrams ( )— ,
, , and —of the medication were used. The participants in the experiment were known to experience
migraines. Each participant was randomly assigned one of the four dosages. When the participants experienced a
migraine, they took the assigned medication and recorded the number of minutes it took to experience relief from
the headache. The mean number of minutes it took each group to experience relief was compared.

What were the experimental units in the experiment?

(A) The number of minutes to experience relief
(B) The mean number of minutes it took each group to experience relief
(C) The four dosages
(D) The participants
(E) The relationship between the dosage and the amount of time

13. A chemist for a paint company conducted an experiment to investigate whether a new outdoor paint will last longer
than the older paint. Fifty blocks made from the same wood were randomly assigned to be painted with either the
new paint or the old paint. The blocks were placed into a weather-controlled room that simulated extreme weather
conditions such as ice, temperature, wind, and sleet. After one month in the room, the blocks were removed, and
each block was rated on texture, shine, brightness of color, and chipping. The results showed that the blocks painted
with the new paint generally had higher ratings than the blocks painted with the old paint. However, an analysis of
the results found that the difference in ratings was not statistically significant. What can be concluded from the
experiment?
(A) There is not enough evidence to attribute the higher ratings to the new paint.
(B) The new paint will last longer than the old paint if used on wooden surfaces.
(C) The experiment is inconclusive because blocks from only one type of wood were used.
(D) The experiment is inconclusive because one month is not enough time for paint to weather.
Because the blocks were randomly assigned to the type of paint, there is evidence that the new paint causes
(E)
better ratings than the old paint.

14. Each person in a simple random sample of 2,000 received a survey, and 317 people returned their survey. How
could nonresponse cause the results of the survey to be biased?

Page 4 of 6 AP Statistics
 Test Booklet

Chapter 4 Review

(A) Those who did not respond reduced the sample size, and small samples have more bias than large samples.
(B) Those who did not respond caused a violation of the assumption of independence.
(C) Those who did not respond were indistinguishable from those who did not receive the survey.
Those who did not respond represent a stratum, changing the simple random sample into a stratified random
(D)
sample.
(E) Those who did respond may differ in some important way from those who did not respond.

15. At a certain clothing store, the clothes are displayed on racks. The clothes on each rack have similar prices, but the
prices among the racks are very different. To estimate the typical price of a single piece of clothing, a consumer will
randomly select four pieces of clothing from each rack. What type of sample is the consumer selecting?
(A) A census
(B) A cluster sample
(C) A simple random sample
(D) A stratified random sample
(E) A systematic random sample

16. A dog food company wishes to test a new high-protein formula for puppy food to determine whether it promotes
faster weight gain than the existing formula for that puppy food. Puppies participating in an experiment will be
weighed at weaning (when they begin to eat puppy food) and will be weighed at one-month intervals for one year.
In designing this experiment, the investigators wish to reduce the variability due to natural differences in puppy
growth rates. Which of the following strategies is most appropriate for accomplishing this?
(A) Block on dog breed and randomly assign puppies to existing and new formula groups within each breed.
Block on geographic location and randomly assign puppies to existing and new formula groups within each
(B)
geographic area.
Stratify on dog breed and randomly sample puppies within each breed. Then assign puppies by breed to
(C)
either the existing or the new formula.
Stratify on geographic location of the puppies and randomly sample puppies within each geographic area.
(D)
Then assign puppies by geographic area to either the existing or the new formula.
Stratify on gender and randomly sample puppies within gender groups. Then assign puppies by gender to
(E)
either the existing or the new formula.

17. A study was conducted to evaluate the impact of taking a nutritional supplement on a person’s reaction time. One
hundred volunteers were placed into one of three groups according to their athletic ability: low, moderate, or high.
Participants in each group were randomly assigned to take either the nutritional supplement or a placebo for six
weeks. At the end of the six weeks, participants were given a coordination task. The reaction time in completing the
task was recorded for each participant. The study compared the reaction times between those taking the supplement
and those taking the placebo within each athletic ability level. Which of the following is the best description of the
study?
(A) A randomized block design
(B) A completely randomized design
(C) A matched-pairs design
(D) A randomized observational study
(E) A stratified observational study

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Chapter 4 Review

18. A recent study examined 699 car accidents in Toronto over a fourteen-month period. Records of phone-service
providers were used to determine whether the driver was using a cell phone during or immediately before the
accident. Overall, the researchers found that drivers using cell phones were 4.3 times as likely to have an accident as
drivers who were not using cell phones. The result was statistically significant. Which of the following can be
concluded from this study?
(A) Cell phone use increases the likelihood of a car accident.
(B) There is an association between cell phone use and accidents, but not necessarily a causal relationship.
(C) There is a correlation between cell phone use and accidents, but not necessarily an association.
(D) The association between cell phone use and accidents is negative.
(E) Cell phone use causes more accidents in Canada, but not necessarily in the United States.

19. A regional transportation authority is interested in estimating the mean number of minutes working adults in the
region spend commuting to work on a typical day. A random sample of working adults will be selected from each of
three strata: urban, suburban, and rural. Selected individuals will be asked the number of minutes they spend
commuting to work on a typical day. Why is stratification used in this situation?
(A) To remove bias when estimating the proportion of working adults living in urban, suburban, and rural areas
(B) To remove bias when estimating the mean commuting time
(C) To reduce bias when estimating the mean commuting time
To decrease the variability in estimates of the proportion of working adults living in urban, suburban, and
(D)
rural areas
(E) To decrease the variability in estimates of the mean commuting time

20. The buyer for an electronics store wants to estimate the proportion of defective wireless game controllers in a
shipment of 5,000 controllers from the store's primary supplier. The shipment consists of 200 boxes each containing
25 controllers. The buyer numbers the boxes from 1 to 200 and randomly selects six numbers in that range. She then
opens the six boxes with the corresponding numbers, examines all 25 controllers in each of these boxes, and
determines the proportion of the 150 controllers that are defective. What type of sample is this?
(A) Biased random sample
(B) Nonrandom sample
(C) Simple random sample
(D) Stratified random sample
(E) Cluster random sample

Page 6 of 6 AP Statistics
 P(A or B) = P(A) + P(B) – P(A and B)
Chapter 5 In Class Review
If A and B are mutually exclusive,
1) Given P(A) = .23, P(B) = .47 and events A and B are mutually exclusive
P(A and B) = 0.
a) Find P (A and B)

P(A and B) = P(A) ∙ P(B|A)

b) Find P (A or B)
If A and B are independent,
P(B|A) = P(B)
2) Given P(A) = .23, P(B) = .47 and events A and B are independent
a) Find P (A and B)
𝑷𝑷(𝑨𝑨 𝒂𝒂𝒂𝒂𝒂𝒂 𝑩𝑩)
P(A|B) =
𝑷𝑷(𝑩𝑩)

b) Find P (A or B)

3) Given P(A) = .23, P(B) = .47, P(B|A) = .3 and events A and B are NOT mutually exclusive
a) Find P (A and B)

b) Find P (A or B)

4) In 1912 the luxury liner Titanic, on its first voyage across the Atlantic, struck an iceberg and sank. Some passengers got
off the ship in lifeboats, but many died. The two-way table gives information about adult passengers who lived and who
died, by class of travel. Suppose we choose an adult passenger at random.

a) Given that the person selected was in first class, what’s the
probability that he or she survived?

b) If the person selected survived, what’s the probability that he or

she was a third-class passenger?

c) If you choose a person at random, what’s the probability that he or she was a third-class passenger OR
survived?

d) If you choose a person at random, what’s the probability that he or she was a third-class passenger AND
survived?

e) Are the events “survived” and “third class” independent? Justify your answer with calculations.

19
5) The voters in a large city are 40% white, 40% black, and 20% Hispanic. (Hispanics may be of any race in official
statistics, but here we are speaking of political blocks.) A mayoral candidate anticipates attracting 30% of the white vote,
90% of the black vote, and 50% of the Hispanic vote. Suppose we select a voter at random.

a) Draw a tree diagram to represent this situation.

b) Find the probability that this voter votes for the mayoral candidate. Show your work.

c) Given that the chosen voter plans to vote for the candidate, find the probability that the voter is black. Show
your work.

6) Approximately 10% of the population is left-handed.

a) If two people are randomly chosen, what is the probability that they are both left-handed?

b) If 4 people are randomly chosen, what is the probability that at least one of them is left-handed?

7) In a group of 100 people, 80 speak English, 35 speak French and 28 speak both languages.

a) Construct a Venn diagram to represent this setting.

b) What is the probability that a randomly chosen person only speaks English?

c) What is the probability that a randomly chosen person doesn’t speak French and doesn’t speak English?

d) Are speaking French and speaking English mutually exclusive? Explain.

e) Are the events “speaks English” and “speaks French” independent? Justify your answer with calculations.

20
6.3 Binomial and Geometric Distributions Practice

1. Approximately 8% of males are color blind.

a. What is the probability that in a group of 10 males, 3 are color blind? Show the formula.

b. What’s the probability that in a group of 10 males, there are at most 2 that are color blind? Show
formula or calculator syntax.

c. What’s the probability that in a group of 10 males, there are more than 3 that are color blind? Show
formula or calculator syntax.

d. Let X = the number of color blind people in group of 30 males. Find the mean and standard deviation
for X. Show work.

2. As a special promotion for its 20-ounce bottles of soda, a soft drink company printed a message on the inside
of each cap. Some of the caps said, “Please try again,” while others said, “You’re a winner!” The company
advertised the promotion with the slogan “1 in 6 wins a prize.” Suppose the company is telling the truth and
that every 20-ounce bottle of soda it fills has a 1-in-6 chance of being a winner. Seven friends each buy one
20-ounce bottle of the soda at a local convenience store. Let X = the number who win a prize.

a. Explain why X is a binomial random variable.

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 b. Find the mean and standard deviation of X.

c. The store clerk is surprised when three of the friends win a prize. Is this group of friends just lucky, or
is the company’s 1-in-6 claim inaccurate? Compute P(X ≥ 3) and use the result to justify your answer.

d. Would your answer to part c change if 4 out of the 7 friends won a prize? Compute an appropriate
probability to justify your answer.

3. Isha decides to use a different strategy for the 1-in-6 game in problem 2. She keeps buying one 20-ounce
bottle of soda at a time until she gets a winner.
a. Find the probability she buys exactly 5 bottles. Show formula.

b. Find the probability that she buys no more than 8 bottles. Show formula or calculator syntax.

c. Find the probability that she buys more than 10 bottles. Show formula or calculator syntax.

d. How many bottles can Isha expect to buy before she finds a winner?

e. Suppose it takes 15 bottles for Isha to get a winner. Does she have convincing evidence that the
probability of getting a winning bottle is not 1/6?

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4. Cole is trying to find a date to prom. He decides to randomly ask girls to go to prom until someone says yes.
Suppose the probability of a girl saying yes is 13%.

a. What’s the probability that the 6th girl Cole asks is the first one to say yes? Show formula.

b. What’s the probability that Cole with have to ask 10 or more girls? Show formula or calculator
syntax.

c. What’s the probability that Cole with have to ask fewer than 5 girls? Show formula or calculator
syntax.

d. How many girls should Cole expect to have to ask to prom before one of them says yes? Show
formula.

5. What’s the probability that you have to roll a die more than 10 times before getting a 1?

6. What’s the probability that you get roll a one exactly 2 times in 10 rolls?

7. What’s the probability that you roll a one at least once in 10 rolls?

8. Jessica decides to keep placing a $1 bet on number 15 in consecutive spins of a roulette wheel until she wins.
On any spin, there’s a 1-in-38 chance that the ball will land in the 15 slot.

a. How many spins do you expect it to take until Jessica wins?

b. Would you be surprised is Jessica won in 3 or fewer spins? Compute an appropriate probability to
support your answer.

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