Summative Test in Statistics and Probability Normal Distribution
1. What do you call a distribution of a continuous random variable whose graph is a bell – shaped?
A. Normal Curve
B. Normal Distribution
C. Standard Distribution
D. Standard Normal Distribution
2. Which of the following best describes standard normal distribution?
A. A distribution which is bimodal.
B. A distribution with a bell – shaped curve.
C. A distribution where its curve is symmetric to the y – axis.
D. A distribution with a mean of 0 and standard deviation of 1.
3. What are the two factors that affect the graph of a normal distribution?
A. Mean and Median
B. Mean and Mode
C. Mean and Standard Deviation
D. Mean and Range
4. Listed below are the properties of a normal distribution except______.
A. Its curve is bell – shaped.
B. Its distribution is unimodal.
C. The probabilities are always equal.
D. Its curve is asymptotic with respect to x – axis.
For items numbers 5 – 7, refer to the table for the standard normal probabilities.
5. What is the area below z=-1
A. 0.1587
B. 0.1376
C. 0.2346
D. 0.4792
6. What is the area above z = -1.64
A. 0.9459
B. 0.9495
C. 0.9549
D. 0.9594
7. What is the area between z = -1.65 and z = 1.65
A. 0.1009
B. 0.10 90
C. 0.9001
D. 0.9010
8. What is the area between 𝑧 = 0.35 and 𝑧 = 2.32?
A. 0.0102
B. 0.3530
C. 0.3632
D. 0. 6266
9. Former ISU basketball player Kelvin Cato is 80 inches tall. Assuming that heights follow approximately a normal
distribution with mean 70 and standard deviation σ=4. What is his corresponding z – score?
A. 1.0
B. 1.5
C. 2.0
D. 2.5
For nos. 10 – 12, refer to the problem below.
The scores of a group of students in a standardized test are normally distributed with a mean of 60 and standard
deviation of 8. Answer the following:
10. How many percent of the students got below 72?
A. 90.33%
B. 92.23%
C. 93.32%
D. 95%
11. What part of the group scored between 58 and 76?
A. 55.59%
B. 57.55%
C. 57.59%
D. 59.59%
12. If there were 250 students who took the test, about how many students scored higher than 64?
A. 72 students
B. 75 students
C. 77 students
D. 79 students
For items nos. 13 – 15 consider the following case.
The length of time it takes a Grade 11 student to play Mobile Legend follows a normal distribution with a mean of
3.5 minutes and a standard deviation of 1 minute.
13. What is the probability that a randomly selected Grade 11 student will play one game of Mobile Legends in less
than 3 minutes?
A. 0.3551
B. 0.3085
C. 0.2674
D. 0.1915
14. What is the probability that a randomly – selected Grade 11 student will take between 2 and 4.5 minutes to play
Mobile Legends?
A. 0.0919
B. 0.2255
C. 0.4938
D. 0.7745
15. At what point in the distribution of times to play Mobile Legends in which 75.8% of the Grade 11 students
exceed when playing game?
A. 2.8 minutes
B. 3.2 minutes
C. 3.4 minutes
D. 4.2 minutes
For items nos. 16 – 18, refer to the situation below.
The scores of students in the 2nd quarter examination in Mathematics has a mean of 32 and a standard deviation of
5.
16. What is the corresponding z – score of 37?
A. 0
B. 1
C. 2
D. 3
17. What is the area below the score of 37?
A. 0.3814
B. 0.4813
C. 0.8413
D. 0.8431
18. What is the area above the score of 37?
A. 0.1569
B. 0.1587
C. 0.5187
D. 0.6186
19. A random variable X has a mean of 4 and standard deviation of 2. Find the corresponding z – score for x=7.
A. 𝑧 = −1.5
B. 𝑧 = −1.0
C. 𝑧 = 1.0
D. 𝑧 = 1.5
20. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that
Z is less than 1.15 is ______.
A. 0.8594
B. 0.8699
C. 0.8749
D. 0.8889