3RD QUARTER EXAMINATION (STATISTICS AND PROBABILITY)

NAME: _______________________________________________________________ SCORE: ___________________

GRADE/SECTION: ________________________________ TIME: _______________ DATE: ____________________

TEST 1
DIRECTIONS: Read and analyze the following statements carefully. Choose the letter of the best answer. Write
the chosen letter on a separate sheet of paper.
1. Which of the following is a discrete random variable?
a. Length of wire ropes c. Number of soldiers in the troop
b. Amount of paint used in repainting the building d. Voltage of car batteries
2. These are two values that describe how scattered or spread out the scores are from the mean value of the random
variable.
a. variance and standard deviation
b. parameter and statistic
c. probability and statistics
d. mean and variance
3. What is the mean of the probability distribution involving the random variable X that gives the number of heads
that appear after tossing four coins once.
a. 1 b. 2 c. 3 d. 4
4-6. When three coins are tossed once, the probability distribution for the random variable X representing the
number of heads that occur is given below.

0 1 2 3
1/8 3/8 3/8 1/8

4. What is the value of the mean?

a. 1 b. 2 c. 1.50 d. 2.5
5. What is the value of the standard deviation of the probability distribution?
a. 0.87 b. 0.75 c. 0.93 d. 0.57
6. What is the value of the variance of the probability distribution?
a. 0.57 b. 0.75 c. 0.87 d. 0.78
7. Which of the following illustrations represents normal distribution?
a. c.

b. d.

8. It is a numerical quantity that is assigned to the outcome of an experiment.

a. random variable c. variable
b. probability d. probability distribution
9. How many ways can a "double" come out when you roll two dice?
a. 2 b. 6 c. 8 d. 12
10. The following statements are true, EXCEPT,
a. A discrete random variable has a countable number of possible values.
b. A random variable is a qualitative variable which values depends on change.
c. A continuous random variable can assume an infinite number of values in one or more intervals.

d. A random variable is a result of chance event, that you can measure or count.
11. Two balls are drawn in succession without replacement from an urn containing 5 orange balls and 6 violet balls.
Let V be the random variable representing the number of violet balls. Find the values of the random variable V.
a. 4, 5, 6 b. 1, 2, 3 c. 0, 1, 2 d. 0, 1, 1, 2
12. Which formula gives the probability distribution shown by the table?

X 5 3 1
a. P( X )= b. P( X )= c. P( X )= d. P( X )=
4 X X X

13. It is the number of times the data appears or repeat in the sequence.
a. frequency b. probability c. distribution d. values
14. Find the mean of the probability distribution involving the random variable X that gives the number of heads
that appear after tossing three coins once.
a. 3.0 b. 1.625 c. 1.50 d. 2.15
15. The variance of the number of cars sold per day is 1.56 and the standard deviation is _______.
a. 2.34 b. 1.52 c. 2.43 d. 1.25
16. The population variance is determined using the formula:

a. σ = ∑(x − µ)2p(x) b. σ2 = ∑(x − µ)2p(x) c. σ =√ ∑(x−µ) ² p (x) d. μ= ∑(x −

2
µ) p(x)

17. What is another name for normal distribution?

a. Gaussain Distribution c. Gaussian Distribution
b. Gassiun Distribution d. Gaushian Distribution
18. The probabilities that a printer produces 0,1,2, and 3 misprints are 42%, 28%, 18%, and 12% respectively. What
is the mean value of the random variable?
a. 1 b. 2 c. 3 d. 4
19. The _____________ of the sampling distribution of the samplemeans is equal to the mean of the population.
a. mean c. standard deviation
b. variance d. probability distribution
20. What percent of the area under a normal curve is within 3 standard deviations?
a. 68.3% b. 94.5% c. 97.9% d. 99.7%
21. A population consists of the five numbers 2, 3, 6, 10 and 12. Consider samples of size 2 that can be drawn from
this population. How many possible samples can be drawn?
a. 5 b. 10 c. 15 d. 20
22. The Central Limit Theorem says that the sampling distribution of the sample mean is approximately normal if
__________.
a. the sample size is large. c. all possible sample are selected.
b. the standard error of the sampling mean is small. d. none of the above.
23. According to Central Limit theorem, which sample size will give a smaller standard error of the mean?
a. 7 b. 12 c. 23 d. 40
24. The mean of the sampling distribution of the sample means according to the Central Limit Theorem is
__________.
a. exactly equal to the population mean.
b. close to the population mean if the sample size is large.
c. equal to the population mean divided by the square of the sample size.
d. cannot be determined.
25. What is the other term for t-distribution?
a. Z-distribution c. Probability distribution
b. Percentile distribution d. Student’s t-distribution
26. Which of the following is NOT a characteristics of t-distribution?
a. Like the normal distribution, the t-distribution has a smooth shape.
b. Like the normal distribution, the t-distribution is symmetric. If you think about folding it in half at the
mean, each side will be the same.
c. Like a standard normal distribution (or z-distribution), the t - distribution has a mean of one.
d. The normal distribution assumes that the population standard deviation is known. The t-distribution does
not make this assumption.
27. This refers to the maximum number of logically independent values, which vary in the data sample.
a. Level of significance c. Percentiles
b. Degree of freedom d. Confidence Level
28. If a population is not normally distributed, the distribution of the sample means for a given sample size n will
____________.
a. be positively skewed.
b. be negatively skewed.
c. take the same shape as the population.
d. approach a normal distribution as n increases.
29. What is the right-tailed area if the confidence interval is 75%?
a. 0.05 b. 0.025 c. 0.25 d. 0.50
30. In a certain barangay, Mario wants to estimate the mean weight µ, in kilograms, of all seven-year-old children
to be included in a feeding program. He wants to be 99% confident that the estimate of µ is accurate 0.05 kg.
Suppose from a previous study, the standard deviation of the weights of the target population was 0.6 kg, what
should the sample size be? Take note the confidence coefficient for 99% confidence level is 2.58.
a. 958.52 b. 463 c. 462.25 d. 959

TEST 2
Direction: Determine the statement whether it is true or false. Write T if the statement is true and F if it is false.
Write your answer on a separate sheet of paper.
31. Cluster sampling is sometimes referred to as area sampling and applied on a geographical basis.
32. Lottery sampling is a sampling technique in which each member of the population has no equal chance of being
selected.
33. Quota Sampling is a sampling where the participants in the study were tasked to recruit other members for the
study.
34. The value of a parameter can be approximated and is not necessarily equal to the statistic of a sample.
35. A statistics is a number which describes a sample.

TEST 3
PROBLEM SOLVING:
A. Two balls are drawn in succession without replacement from an urn containing 5 orange balls and 6 violet balls.
Let V be the random variable representing the number of violet balls.
36. List the sample space.
37. Find the values of the random variable V.
38. Construct the frequency distribution of the values of the random variable V.
39. Construct the probability distribution of the random variable V by getting the probability of occurrence
of each value of the random variable.
40. Construct the probability histogram.
B. For Item 41-45: Solve the problem below.
Given that the population mean is equal to 20 and the standard deviation is 3. Between what two values
would the middle 75% of the scores fall? Draw the graph representing the corresponding area.
C. For Item 46-50: Solve the problem below.
An electrical company claims that the average life of the bulbs it manufactures is 1 200 hours with a
standard deviation of 250 hours. If a random sample of 100 bulbs is chosen, what is the probability that the
sample mean will be between 1150 hours and 1 250 hours? Draw a graph and plot the z-score and its
corresponding area. Then, shade the part that you’re looking for.