STATISTICS AND PROBABILITY
SUMMATIVE EXAMINATION # 1
QUARTER 4
NAME: ____________________________________ GRADE AND SECTION: _____________ SCORE: _____
I. DIRECTION. Read the questions carefully. Choose the letter that corresponds to the correct
answer and write it on the space provided before the number. Write ‘E’ if your answer is not
among the choices.
1. The distribution of the data where the mean, median, and mode are approximately
equal and where the data is clustered closely around the center, and it is called the __.
a. Probability Distribution c. Normal Probability Distribution
b. Central Tendency d. Variability
2. What is the total area around the normal curve?
a. 0.25 b. 0.5 c. 0.75 d. 1.0
3. Which of the following is NOT a property of a normal curve?
a. The curve is symmetric above zero.
b. The curve extends indefinitely in one direction.
c. The total area under the normal curve is equal to 100%.
d. The area can be determined based on the standard score or z=score.
4. What is the z-score of X = 90, when 𝜇 = 95.3 and 𝜎 = 3?
a. 2.37 b. -2.55 c. -1.77 d. 1.77
5. What is the area under the normal curve bounded by X = 90, when 𝜇 = 95.3 and 𝜎 = 3?
a. 0.4616 b. 0.4608 c. -0.4616 d. -0.4608
6. What is the area under the normal curve to the left of z = -2.02?
a. 2.17% b. 2.18% c. 2.27% d. 2.28%
7. Given that X = 65, 𝜇 = 55, and 𝜎 = 5, what is the z-score?
a. 0.1 b. 0.2 c. 1 d. -1
8. Which of the following is the area under the normal curve bounded by z > -2.02?
a. 97.80% b. 97.81% c. 97.82% d. 97.83%
9. What is the area under the standard normal curve bounded by z = -1.05 and z = 2.25?
a. 84.09% b. 84.10% c. 84.11% d. 84.12%
10. What is the area under the standard normal curve bounded by z = 0.92 and z = 1.3?
a. 8% b. 8.1% c. 8.2% d. 8.3%
II. PROBLEM SOLVING
A. Find the value of z and X under the normal curve when:
a. 𝜇 = 65, 𝜎 = 9, and the area is equal to 79.5%.
b. To the left of the mean, 𝜇 = 58, 𝜎 = 7, and A = 0.4474
B. Determine each of the following areas and show these graphically. Use probability
notation in your final answer.
1. Above z = 1.46
STEPS SOLUTION
1. Draw the normal curve
2. Locate the z-value
3. Draw a line through z-value
4. Shade the required region
5. Consult the z-table and find the area
that corresponds to z = 1.46
6. Examine the graph and use the
probability notation to form an
equation showing the appropriate
operation to get the required area
7. Make a statement indicating the
required area.
2. Find the area between z = -1.32 and z = 2.37
STEPS SOLUTION
1. Draw the normal curve
2. Locate the z-value
3. Draw a line through z-value
4. Shade the required region
5. Consult the z-table and find the area
that corresponds to z = -1.32 and
z = 2.37
6. Examine the graph and use the
probability notation to form an
equation showing the appropriate
operation to get the required area
7. Make a statement indicating the
required area.
Prepared by:
MARITES O. DE LEON
Teacher III
MARLON B. DIZON
Teacher II
