MIDTERM EXAMINATION

STATISTICS AND PROBABILITY

Name: Date:

Grade & Section: Score:

General Direction: Read and follow the given directions, failure to follow it, will lead to
deduction of points. Use the given questionnaire as your answer sheet and for numbers that
needs to be solved you have to show your solution at the back portion of the test paper or
utilized another answer sheet and attached it right after answering. Answer it honestly!

I. Multiple Choice
Direction: Read and understand the following statements/questions and write the letter of your
choice on the space provided before the number.

________1. A discrete probability distribution is also called as _____________________.

A. Probability mass function C. Probability mass index

B. Probability mass D. Random Variable

2. Discrete variable is from qualities that can be

A. Measured C. Both A and B
B. Counted D. none of these
3. These are unknown value which is often designated by letters and can be classified as
discrete or continuous.

A. Random Experiment C. Random Variable

B. Random Sample D. Random process
4. It is the weighted average of the possible values that the random variable can take.
A. Variance C. Standard Deviation
B. Mean D. Function
5. The formula for calculating the Z-score of a population data is________________.

X−μ X− X
A. z= C. z=
σ z
X− X X−μ
B. z= D. z=
s S
6. The _____________ of the curve is determined by the standard deviation of the
distribution.
A. width B. dimension C. top D. limit

7. What is the other term of z table?

A. Table of Areas of Geometric Figure C. Table of Contents
B. Table of Areas Under the Normal Curve D. Periodic Table

8. It is a measure of relative standing and a descriptive measure of the relationship of a

measurement to the rest of the data.
A. Mean B. Quartile C. Percentile D. Average

9. It is a sampling method of choosing representatives from the population wherein

every sample has an equal chance of being selected.
 A. Random Sampling C. Sampling Technique
B. Random Method D. Stratified random sampling

10. Which of the following is a statistic?

A. µ B. σ2 C. s2 D. σ

11. The total area under the standard normal curve is _________.
A. -1 B. 0 C. 0.5 D. 1

12. Which of the following statements is correct?

A. The mean of the sampling distribution of the sample means is greater than
the population mean.
B. The mean of the sampling distribution of the sample means is lesser than
the population mean.
C. The mean of the sampling distribution of the sample means is always equal
to the population mean.
D. The mean of the sampling distribution of the sample means maybe equal,
greater than or lesser than the population mean.
13. Which of the following is NOT a discrete variable?
A. The number of students present in a class
B. The number of death per year attributed to kidney failure
C. The average amount of water consumed per household per month
D. The number of patients in a hospital each day

14. If two coins are tossed, which is not a possible value of the random variable for the
number of tails?
A. 0 B. 1 C. 2 D. 3

15. Which of the following is NOT a true statement?

A. The value of a random variable could be zero.
B. Random variables can only have one value.
C. The probability of the value of a random variable could be zero.
D. The sum of all the probabilities in a probability distribution is always equal to
one.

16. Which of the following is a NOT continuous variable?

A. A person’s weight each year
B. A person’s height on each birthday
C. Number of bicycle finished in a factory each day
D. The amount of water in a pale
17. Which of the following is a discrete random variable?
A. the average amount of electricity consumed
B. the number of patients in a hospital
C. the amount of paint used in repainting a building
D. the average weight of female athletes

18. In a local community, couples were asked the questions “Are you satisfied with the
work of the current president?” If the husband and the wife both said “yes”, the response is
written as YY. If the husband said yes and the wife said “no”, the response is YN. Let X = the
number of “yes” responses, what are the possible values of the random variables?

A. 0, 1, 2 C. 2, 3, 4
B. 1, 2, 3 D. 1, 1, 2
 19. What is the sum of the probabilities of all values of the random variable?
A. Σ P(X) = 1 C. Σ P(X) = 0
B. Σ P(X) = 1/10 D. Σ P(X) = 10

20. Which of the following can serve as the values of a probability distribution?
A. P(1) = 0.42, P2) = 0.31, P(3)= 0.37
B. P(1) = 9/14, P2) = 5/14, P(3)= 1/14
C. P(1) = 0.08, P2) = 0.12, P(3)= 0.83
D. P(1) = 10/33, P2) = 1/3, P(3)= 12/33
X
21. If P(X)= , what are the possible values of X for it to be a probability distribution?
8
A. 0, 2, 3, 4 C. 1, 3, 4
B. 0, 1, 2, 3 D. 1, 2, 3
22. The probability of each value of the random variable must be
A. between or equal to 0 and 1
B. greater than 1
C. between 1 and 2
D. greater than 2

(For numbers 23-24) In a recent Barangay Basketball League, each player went to free throws 2
times. The number of free throws made by each player is described by the following probability
distribution.

Probability
Number of free throws, X
P(X)
0 0.20
1 0.45
2 0.35

23. What is the mean of the probability distribution?

A. 1.00 C. 2.00
B. 1.15 D. 2.25

24. What is the variance of the probability distribution?

A. 0.5725 C. 0.2575
B. 0. 7255 D. 0.5275

25. Which of the following statements is TRUE about the interpretation of the values of
variance and standard deviation?
A. A small value of variance or standard deviation indicates that the distribution of the
discrete random variable is closer about the mean.
B. A large value of variance or standard deviation indicates that the distribution of the
discrete random variable is closer about the mean.
C. A small value of variance or standard deviation indicates that the distribution of the
discrete random variable takes some distance from the mean.
D. All of the above.

26. If the average age of retirement for the population in the Philippines is 65 years and
with standard deviation of 5 years, what is the approximate age range in which 68% of people
retire?

A. 55 – 60 years B. 55 – 65 years C. 60 – 65 years D. 60 -70 years

 27. Find the area of the shaded region of the given figure.

A. 0.0865 B. 0.3907 C. 0.4772 D. 0.8413

28. What is the area between z = - 1.23 and z = 2?

A. 0.0865 B. 0.4772 C. 0.8679 D. 0.8779

For numbers 29 and 30: The Philippine High School has 1,500 grade 10 students. Mr.
Manalo, the principal, wants to obtain information from the students as to the result of the
Mathematics part in NCAE. Based from 500 sample students surveyed, it was found out that the
mean falls on 65.80 in the said area.

29. What do 1500 grade 10 students signify?

A. statistic B. sample C. population D. parameter

30. What does the value 65.80 denote?

A. statistic B. sample C. population D. parameter

31. If a sample is drawn from a population, what happens to the standard error of the
mean if the sample size is increased from 50 to 200?
A. The standard error of the mean remains the same.
B. The standard error of the mean will also increase.
C The standard error will decrease.
D. The standard error will either increase or remains the same.

32. Which of the following best describe variable that can be measured?
A. Discrete B. Continuous C. Nominal D. Qualitative

II. EVALUATION

A. Construct a probability distribution for the data and draw a histogram of distribution.

33. The probabilities that a surgeon operates on 3, 4, 5, 6, or 7patients in any day are 0.15, 0.20,
0.25, 0.20, and 0.20, respectively.
34. Complete the table below. Then, evaluate the mean and variance.

Number
Probability X ∙ P (X ) X −μ 2
(X −μ)
2
(X −μ) ∙ P (X )
of Cars
P(X)
Sold X
1
0
10
2
1
10
3
2
10
2
3
10
2
4
10
2
μ=¿ σ =¿

35. Find the area above z = 2.14 (Follow the steps and sketch it in a normal curve).

36. Evaluate the problem using the population formula.

Given the mean μ = 50 and the standard deviation, σ = 4 of a population of Reading

scores. Find the z-value that corresponds to a score X = 58.