R epublic of the P hilippines
D epartment of E ducation
N a t i o n a l C a pi t a l Re g i o n
Sc h o o l s D i v i s i o n O f f i c e o f La s Pi ñ a s C i t y
NAME: _________________________________________________ Score: _________________
GRADE & SECTION ____________________________________ Teacher: _______________
SELF-LEARNING ASSESSMENT
STATISTICS AND PROBABILITY
MATHEMATICS 11
THIRD QUARTER
DIRECTION: Read each item carefully. Blacken the circle of the correct
answer in the answer sheet.
1. Which of the following represents a discrete random variable?
A. The weight in kilograms of randomly selected Academic Track students
B. The time it takes a student to finish answering the supplementary activity sheet.
C. The number of people who experience side effects after COVID vaccination.
D. A patient’s body temperature reading in °C.
2. Which of the following is an example of a continuous random variable?
A. The number of passengers in a public utility jeep going to Alabang.
B. The amount of rainfall in Las Piňas within a month.
C. The number of students enrolled in a senior high school year 2020-2021.
D. The number of red marbles in a jar.
3. An urn contains 7 balls. Each ball is labelled with numbers 0, 1, 2, 3, 4, 5, and 6. A
person randomly draws one ball. Let X be the random variable for the number on the ball.
What possible values can be assigned to the random variable X?
A. X= { 0, 2, 3, 4, 5, 6 } C. X= { 0, 1, 2, 3, 4, 5 }
B. X= { 0, 1, 2, 3, 4, 5, 6 } D. X= { 1, 2, 3, 4, 5, 6 }
4. Which of the following is NOT an example of a random variable?
A. Winning in a raffle draw C. Winning in a singing contest
B. Celebrating your birthday D. Rolling dies
5. Applying the Properties of a Discrete Probability Distribution, which of the following
tables DOES SUGGEST a probability distribution for a random variable?
A.
X 1 2 3 4 5
P(X) 1/11 1/11 1/11 1/11 1/11
B.
X 1 2 3 4 5
P(X) 1/14 4/14 1/14 1/14 7/14
C.
X 1 2 3 4 5
P(X) 10 15 20 25 30
D.
X 1 2 3 4 5
P(X) 0.13 0.05 0.003 0.23 0.35
6. In tossing two coins, what is the probability of getting all heads?
1 1 1 1
A. B. C. D.
2 3 4 5
7. In rolling a die, what is the probability of getting even number?
1 1 1 1
A. B. C. D.
2 3 4 5
Refer to the given table below in answering numbers 8-9.
No of tails 0 1 2 3
P(x) 0.125 0.375 0.375 0.125
8. What is the sum of the probability of the given probability distribution?
A. 1 B. 0 C. -1 D. 0.375
9. What is the P (1) ● P (2)?
A. 0.0467 B. 0.1406 C. 0. 25 D. 0. 75
10. The random variable A representing the number of Almonds in
a chocolate bar have the following probability distribution.
A 0 1 2 3 4
P(A) 2/20 6/20 4/20 5/20 x
What is the value of x?
A. 3/20 B. ¼ C. 1/5 D. cannot be determine
11. Let G be a random variable defining number of students who are
always absent in the class of General Math.
G 3 4 5
P(G) 0.5 0.1 0.4
What is the mean of G from the given table?
A. 3.9 B. 1.5 C. 1 D. 3
12. If you have a very small variance or standard deviation but not equal
to zero, it states that
A. the data points are farther from the mean.
B. the data points are nearer to the mean.
C. The data points are equal to the mean.
D. The data points have no relationship with the mean.
For number 13 - 14
The following data shows the probability for the number of Casuy candy
sold in a given day at South Station Pasalubong Center.
Number of dozen of 10 13 16 19 22
Casuy candy sold each
day (𝑥)
P(x) 0.3 0.2 0.2 0.15 0.15
2
13. How many dozen of Casuy candies should be expected to sold per day?
A. 12 B. 15 C. 17 D. 18
14. What is P( x > 22)
A. 0. 85 B. 0.15 C. 1 D. 0
15. The total area under the normal curve is
A. -1 B. 0.5 C. 1 D. 0
16. What can you say about the mean and standard deviation of the
given figure below?
A. The Mean are Equal, but the standard deviations are not equal.
B. The mean are not equal but the standard deviations are equal.
C. Both the mean and the standard deviations are not equal.
D. Both mean and standard deviations are equal.
For nos. 17- 20, refer to the problem:
“Because of Covid-19 pandemic, the IATF are limiting the number of customers in a
restaurant under the MECQ areas. Only 20% of their available chairs the costumers are
allowed to enter in their establishment. Mr. Kurt computes the probabilities for the
number of costumers going-in each day in his restaurant. The discrete probability
distribution is shown below”
X P(X) X P(X) X2 X2 P(X)
1 0.01
2 0.08
3 0.14
4 0.22
5 0.45
6 0.10
17. By completing the above table, what is the mean number of costumers
going-in each day in his restaurant?
A. 3.67 B. 4.77 C. 2.87 D. 4.32
18. By completing the above table, what is the variance of the number of
costumers going-in each day in his restaurant?
A. 1.30 B. 1.65 C. 2.35 D. 3.16
19. What is the standard deviation of the number of costumers going-in
each day in his restaurant?
A. 1.09 B. 1.14 C. 1.28 D. 1.78
20. What would be the best interpretation of the mean number of costumers
3
going-in each day in his restaurant?
A. During MECQ, most of the day there are 3 costumers going-in in his restaurant.
B. During MECQ, in 100 days, exactly 432 costumers are going-in in his restaurant.
C. During MECQ, if we look at the large number of days, then each day,
approximately about 4 persons going-in in his restaurant.
D. None of these.
21. If the average age of retirement of public employees is 62 years with a
standard deviation of 3 years, what is the approximate age range in
which 68% of people retire?
A. 56- 66 B. -53- 71 C. 59 – 65 D. 62- 65
22. Which of the following is NOT a property of a standard normal curve?
A. The distribution curve is bell-shaped.
B. The curve is symmetrical about its center.
C. The mean, the median, and the mode coincide at the center.
D. The tails of the curve flatten out definitely along the horizontal axis.
23. What is the area that corresponds to z = -1.25 under the normal curve?
A. 0.3944 B. -0.3944 C. 0.3289 D. 0.3289
24. What is the area between z = -2.0 and z = 2.0 under the normal curve?
A. 0.9322 B. 0.9544 C. 0.9677 D. 0.9733
25. What is the z-score of an area of 0.9370 under the standard normal
curve?
A. z = - 1.53 B. z =1.53 C. z = -2.53 D. z = 2.53.
26. If x-value follows a normal distribution with mean 15 and standard
deviation 3, what is the z-value of x = 9?
A. -1 B. -2 C. -3 D. 1
27. The scores of the students in the final examination are normally distributed with a mean
of 72 and a standard deviation of 8. What score do you find the upper 10% of the
students’ scores?
A. 80 B. 82 C. 84 D. 86
28. _________ is the measurement or quantity that describes the population.
A. Means B. Parameter C. Sample D. Statistics
29. A population consists of the values (1, 2, 3) drawn with a sample of size 2.
What is the mean of the sampling distribution of the sample means?
A. 1.00 B. 2.00 C. 3.00 D. 4.00
4
30. Suppose three coins are tossed. Let Y be the random variable representing the number of
tails that occur. What would be the possible value of the random variable Y?
A. 4, 3 2, 1 C. 3, 2, 1, 0
B. 2,1, 0 D. Cannot be determined
31. The average weight of the whole class under study is 58 kg. The
underligned words is the ________________.
A. parameter C. sample
B. population D. Statistics
32. Which method is most likely to produce a random sample of the members
of your class?
A. Listing the first five students that comes to mind.
B. Choosing the five oldest students in the class.
C. Writing the name of each student on a separate piece of paper
and then pull out these slips from a hat.
D. Selecting the first six students to arrive at class.
33. It is calculated by dividing the sum of the observations by the total
number of observations.
A. Mean C. Parameter
B. Variance D. Standard deviation
34. What is true among the following statements.
A. As the sample size increases, the variance of the sample mean increases.
B. As the sample size decreases, the variance of the sample mean decreases.
C. As the sample size increases, the variance of the sample mean decreases.
D. As the sample size increases, the variance of the sample mean increases.
35. From the given set of data below, find the sample variance.
9, 13, 15, 18, 20
A. 18 B. 18.5 C. 19 D. 19.5
36. What formula of SE should be used when the variance is known in the sampling
distribution of sample mean for normal population?
2 2
σ s s σ
A . σ x= B. sx= C . sx= D. σ x =
√n √n √n √n
37. Which theorem states that “If random samples of size n are drawn from
a population, then as n becomes larger, the sampling distribution of
mean approaches the normal distribution, regardless of the shape of
the population distribution”?
A. Discrete Limit Theorem C. Central Limit Theorem
B. Phytagorean Theorem D. Variance Limit theorem
38. The distribution is approximately normal if n≥30 regardless of the shape of distribution.
If n ≤30, the sample mean is also approximately normal as long as the population is
normally distributed.
5
A. True C. False
B. Sometimes True D. Either true or false
39. The sample distribution of the mean is a distribution of
A. Individual population values C. Sample statistic
B. Individual sample values D. Population parameter
40. What can you say about the mean of the sampling distribution of a population with a
mean of 50 and with a standard deviation of 3 which drawn with a random sample of 10
measurement?
A. It is equal to the population mean.
B. It is greater than the population mean.
C. It is less than the population mean.
D. Cannot be determined.
41. A population has a normal distribution with a mean of 50 and a standard deviation of
10. If a random sample of size 9 is taken from the population, then what is the
probability that this sample mean will be between 48 and 54?
A. 0.060 B. 0.228 C. 0.385 D. 0.611
42. A random sample of size 25 is to be selected from a normal population having a mean
of 81 and a variance of 9. What is the 95th percentile of the sampling distribution of the
mean?
A. 80.01 B. 81.99 C. 82.13 D. 82.18
43. A random sample of size 16 is to be selected from a normal population having a mean
of 100 and a variance of 9. What is the 90th percentile of the sampling distribution of
the mean?
A. 97.44 B. 100.08 C. 100.32 D. 100.64
44. Which of the following is property of the t-distribution?
A. It is symmetric
B. As the sample grows, it gradually approaches the normal distribution.
C. It’s exact shape is characterized by the degrees of freedom
D. All of the above are properties of the t-distribution.
45. What is the other term used for confidence interval?
A. Alpha C. Interval estimate
B. Margin of error D. Degree of confidence
σ
46. In estimating population mean, the z𝛼/2 ( ) in the formula is _____.
√n
A. Population mean C. z-value
B. Margin of error D. Standard deviation
47. Find the 95% confidence interval estimate of population mean given
the standard deviation of 8, sample size of 60, and sample mean of 28.
A. 25.981 < 𝜇 < 30.019 C. 5.981 < 𝜇 < 10.019
6
B. 57.981 < 𝜇 < 62.019 D. 92.981 < 𝜇 < 97.019
48. How will you compute for q^ if ^p is given?
A. 1 + ^p B. 1 / ^^p. C. 1 * ^p D. 1 - ^p
49. What is the required sample size if the ^p = 0.45, E = 0.5 and confidence
level is 99%?
A. 5 B. 6 C. 7 D. 8
50. If the sample size is 23 and σ is given, what is the most appropriate
formula to estimate the confidence interval?
A. C.
B. D.
Answer Key
1 C 26 B
2 B 27 B
3 B 28 B
4 B 29 B
5 B 30 C
6 C 31 B
7 A 32 C
8 A 33 A
9 B 34 C
10 A 35 B
11 A 36 D
12 B 37 C
13 B 38 A
14 A 39 C
15 C 40 A
16 A 41 D
17 D 42 B
18 A 43 D
19 B 44 D
20 C 45 C
21 C 46 B
7
22 D 47 A
23 A 48 D
24 B 49 C
25 B 50 B
