Practice Problems Quiz # 1

Please Note: You are not responsible for questions 20, 25, 26, 27, 28, 29, 38, 39, 40 for Quiz # 1.

1. A customs agent rolls an ordinary die as each traveler arrives at the customs station. If
the die comes up 6 the traveller’s luggage is searched thoroughly. Otherwise, the
traveler is allowed to pass without a thorough search. Which one of the following is
correct?

A) One out of every 6 travelers receives a thorough search.

B) After many travelers have gone through customs, about 60% of them will have
been subjected to a thorough search.

C) After many travelers have gone through customs, about 12.5% of them will have
been subjected to a thorough search.

D) Five out of every six travelers is allowed to pass without a thorough search.

E) None of the above.

2. There are 150 women in a group of college graduates. Another group consists of 800
women who ended their education after graduating from high school. Which of the
following tools would be best suited for comparing starting salaries for the two
groups?

A) Cumulative distribution plot.

B) Dotplots

C) Stem-and-leaf diagrams

D) Frequency Histograms

E) Box plots
3. A dataset of 23 values of a variable has a mean of 10.8 and a standard deviation of 3.2
The third data value is 9.2. What is the value of the deviation from the mean for this
third data value?

A) (9.2 – 10.8)/3.2

B) (9.2 – 10.8)2

C) (9.2 – 10.8)2/22

D) (9.2 – 10.8)2/23

E) (9.2 – 10.8)

4. Incomes were reported in whole thousands of dollars. The histogram of the incomes
is shown below. Based on the histogram, what percent of incomes are above 17
thousand dollars?

Histogram of Income N = 10

Midpoint Count
10.00 1 *
15.00 5 *****
20.00 3 ***
25.00 1 *

A) 10

B) 20

C) 30

D) 40

F) None of the above

5. Outliers (extreme observations large of small) affect the following:

I. The median
II. The interquartile range
III. The quartiles

A) I and II only

B) II and III only

C) I and III only

D) I, II, and III

E) None of the above.

6. For any set of data, the sum of the deviations from the mean is zero.

A) True B) False

7. A histogram based on many narrow class intervals will fail to show the overall pattern
in a distribution.

A) True B) False

8. A skewed distribution has left and right sides that are mirror images of one another.

A) True B) False

9. For the data 4, 2, 10, 8, what is the value of the sum of squared deviations from the
mean?

A) 0

B) 6

C) 40

D) 184

E) None of the above

10. The mean annual income of 20 women is $22,000 and the mean annual income of 10
men is $19,000. What is the mean annual income of the combined group of 30 people?

A) $19,000

B) $20,000

C) $21,000

D) $22,000

E) None of the above.

11. Longitudinal data were collected on a continuous variable but they were given to us
only in numerical order from smallest value to largest value rather than in time order.
Which of the following could we produce from data as given?

I. the dotplot
II. the median
III. the sequence plot

A) I and II only

B) II and III only

C) I and III only

D) I, II, and III

E) None of the above

12. A sequence plot of 5 years of monthly data is shown below. Which of the following
best describes the plot?

A) random

B) seasonal

C) straight-line trend

D) straight-line trend
plus seasonal

E) None of the above

13. A sequence plot of 5 years of monthly data is shown below. Which of the following
best describes the plot?

A) random

B) seasonal

C) straight-line trend

D) straight-line trend
plus seasonal

E) None of the above

14. What are the mean and standard deviation for the data sample 4, 7, 5, 9, 5?

A) 5 and 2

B) 5 and 1

C) 6 and 1

D) 6 and 2

E) None of the above.

15. If any set of data is standardized, the standard deviation of the standardized data will
always be 1. (Assume that the original numbers are not all equal to the same value).

A) True B) False
16. According to Business Week magazine, the starting salaries of female MBA
graduates have a mean of $54,749, a standard deviation of $10,250, and a median of
$47,543. Based on this information, the distribution of female MBA graduates
appears to be

A) skewed to the right

B) skewed to the left

C) symmetric

D) mound-shaped

E) None of the above choices represent a suitable response

17. A discrete random variable has the following probability distribution:

x 0 5 10 20
p (x) .1 .6 .1 .2

The expected value of the random variable is

A) 5.0

B) 9.0

C) 10.0

D) 20.0

E) None of the above choices represent a suitable response.

18. If events A and B are independent with P(A) = .6 and P(B) = .4 then

A) P(A ∩ B) = .20

B) P(A ∪ B) = .76

C) P(A ∩ B) = 1.00

D) P(A ∪ B) = .24

E) P(A ∩ B) = 0.00
19. Of 20 applicants for a job, 15 are female and 5 are male. If the two applicants are
selected at random to be interviewed, what is the probability that both interviews will
be granted to men? (Round your answer to 4 decimal places.)

A) .3947

B) .0526

C) .4473

D) .5527

E) .9474

20. The weight of a manufactured product has a normal probability distribution with a
mean of 6 ounces and a standard deviation of 2.5 ounces. Which of the following
statements is true regarding the sampling distribution of x for samples of size n =
15?

A) The mean of the sampling distribution is 6 ounces

B) The standard deviation of the sampling distribution is 2.5 ounces

C) The form of the sampling distribution is approximately normal

D) both (A) and (B)

E) None of the above choices represents a suitable response

21. A random variable is uniformly distributed between 0 and 100. Its mean is

A) 0

B) 100

C) 49.5

D) 50.5

E) None of the above choices represent a suitable response.

22. A discrete random variable is uniformly distributed between 0 and 60. Its variance
is

A) 0

B) 5

C) 25

D) 310

E) None of the above choices represent a suitable response.

23. Two events are such that P(A) = .7, P(B) = .5, and P(A ∩ B) = .30. Events A and
B are

A) independent

B) mutually exclusive

C) dependent

D) complementary

E) None of the above choices represent a suitable response.

24. Ages of five students are: 26, 17, 16, 30, and 21. The median age is

A) 16

B) 22

C) 26

D) 5

E) None of the above choices represent a suitable response.

25. A normal population has a mean of 50 and a standard deviation of 3. At least 95% of
the values in the population must be between

A) 47 and 53

B) 44 and 56

C) 44 and 53

D) 47 and 50

E) None of the above choices represent a suitable response

The following information is for the next two questions: Suppose that, for houses built
prior to 1945, the mean size is 2,000 square feet with a standard deviation of 200 square
feet. Furthermore, 80% of these houses have only one bathroom. For samples of size n =
1,600.

26. The mean of the sampling distribution of x is

A) 2,000

B) 5

C) 80%

D) 1%

E) None of the above choices represents a suitable response.

27. The standard deviation of the sampling distribution of x is

A) 2,000

B) 1,000

C) 5

D) 10

E) None of the above choices represents a suitable response.

28. When samples of size 25 are collected from a normal population that has a mean of
100 and a standard deviation of 20, the sampling distribution of x will have a
standard deviation of

A) 100

B) 4

C) 16

D) 5

E) None of the above choices represents a suitable response

29. When samples of size 10 are collected from a normal population, the sampling
distribution of x will be

A) normal

B) skewed to the right

C) skewed to the left

D) symmetric, but not normal

E) The form of the sampling distribution can not be determined from the information
provided.

30. Suppose that 20% of cars have at least one under-inflated tire. If two cars are
independently selected, at random, what is the probability that both will have at least
one under-inflated tire?

A) .36

B) .40

C) .20

D) .04

E) None of the above choices represents a suitable response.

The following information is for the next two questions: A sample of five graduating
seniors showed that they had the following numbers of job offers: 0, 0, 1, 4, 10. Note
that Σ x = 15 and Σ x2 = 117.

31. The sample mean is

A) 3

B) 23.4

C) 3.75

D) 29.25

E) None of the above choices represents a suitable response.

32. The sample variance is

A) 14.4

B) 14.4

C) 18

D) 18

E) None of the above choices represents a suitable response.

33. Among a large group of patients recovering from shoulder injuries, it is found that
22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of
these. The probability that a patient visits a chiropractor exceeds by 0.14 the
probability that a patient visits a physical therapist. Determine the probability that a
randomly chosen member of this group visits a physical therapist.

A) 0.26

B) 0.38

C) 0.40

D) 0.48

E) 0.62
34. The number of injury claims per month is modeled by a random variable N with
1
P[N = n ] = , where n ≥ 0. Determine the probability of at least one claim
(n + 1)(n + 2)
during a particular month, given that there have been at most four claims during that
month.

1
A)
3

2
B)
5

1
C)
2

3
D)
5

5
E)
6

35. An insurance company issues life insurance policies in three separate categories:
standard, preferred, and ultra-preferred. Of the company’s policyholders, 50% are
standard, 40% are preferred, and 10% are ultra-preferred. Each standard policyholder
has probability of 0.010 of dying in the next year, each preferred policyholder has
probability of 0.005 of dying in the next year, and each ultra-preferred policyholder
has probability of 0.001 of dying in the next year. A policyholder dies in the next
year. What is the probability that the deceased policyholder was ultra-preferred?

A) 0.0001

B) 0.0010

C) 0.0071

D) 0.0141

E) 0.2817
36. The probability that a visit to a primary care physician’s (PCP) office results in
neither lab work nor referral to a specialist is 35%. Of those coming to a PCP’s office,
30% are referred to specialists and 40% require lab work. Determine the probability
that a visit to a PCP’s office results in both lab work and referral to a specialist.

A) 0.05

B) 0.12

C) 0.18

D) 0.25

E) 0.35

37. A study of automobile accidents produced the following data:

Model year Proportion of all vehicles Probability of involvement

in an accident
1997 0.16 0.05
1998 0.18 0.02
1999 0.20 0.03
Other 0.46 0.04

An automobile from one of the model years 1997, 1998, and 1999 was involved in an
accident. Determine the probability that the model year of this automobile is 1997.

A) 0.22

B) 0.30

C) 0.33

D) 0.45

E) 0.50
38. Two instruments are used to measure the height, h, of a tower. The error made by the
less accurate instrument is normally distributed with mean 0 and standard deviation
0.0056h. The error made by the more accurate instrument is normally distributed with
mean 0 and standard deviation 0.0044h. Assuming the two measurements are
independent random variables, what is the probability that their average value is
within 0.005h of the height of the tower?

A) 0.38

B) 0.47

C) 0.68

D) 0.84

E) 0.90

39. An insurance company’s monthly claims are modeled by a continuous, positive

random variable X, whose probability density function is proportional to (1 + x)-4 ,
where 0 < x < ∞. Determine the company’s expected monthly claims.

1
A)
6

1
B)
3

1
C)
2

D) 1

E) 3
40. A probability distribution of the claim sizes for an auto insurance policy is given in
the table below:

Claim Size Probability

20 0.15
30 0.10
40 0.05
50 0.20
60 0.10
70 0.10
80 0.30

What percentage of the claims are within one standard deviation of the mean claim
size?

A) 45%

B) 55%

C) 68%

D) 85%

E) 100%