MDM4U Normal Distribution (z-scores) Worksheet
Multiple Choice
Identify the letter of the choice that best completes the statement or
answers the question.
1. Which of the following is not a property of the standard normal
distribution?
a. the area under the curve is 1
b. the mean is 1
c. the variance is 12
d. the standard deviation is 1
2. For X ~ N (5, 22) the z-score of x = 4.2 is
a. 0.4
b. 0.2
c. 0.2
d. 0.4
3. The z-score corresponding to the 44-th percentile is
a. 2.62
b. 0.15
c. 0.44
d. 4.40
4. Given a normally-distributed data set whose mean is 40 and whose
standard deviation is 8, what value of x would have a z-score of 1.25?
a. 10
b. 10
c. 30
d. 50
5. The heights of men, in centimeters, are normally distributed with a
mean of 175 and a standard deviation of 20. If Mario is 180 cm tall,
what percent of men is he taller than?
a. 0.62%
b. 40.13%
c. 59.87%
d. 99.38%
6. The volume of cola in 355-mL cans is normally distributed with a
standard deviation of 3 mL. What percent of cans have a volume greater
than 359 mL?
a. 9.18%
b. 35.9%
c. 64.1%
d. 90.82%
7. To earn a scholarship, Luc needs to score in the top 8% on an entrance
test. If test marks are normally distributed with a mean of 500 and a
standard deviation of 38, what mark (to the nearest whole number) is he
aiming for?
a. 446
b. 447
c. 553
d. 554
8. If X ~ N (40, 32), what percent of the data are between 36 and 41?
a. 9.18%
b. 18.81%
c. 53.75%
d. 54.38%
9. The number of candies in a bag is normally distributed with a mean of
200 and a standard deviation of 3. In what percentile is a bag with 205
candies?
a. 2-nd
b. 70-th
c. 71-st
d. 95-th
10. The masses of bolts made in a plant are normally distributed. Bolts
will be rejected if their z-scores are greater than 2.15 or less than 2.10.
What percent of bolts will be rejected?
a. 0%
b. 1.58%
c. 1.79%
d. 3.37%
11. The diameters of inflated balloons, in millimeters, are normally
distributed with a mean of 200 and a standard deviation of 12. Balloons
will burst if their diameters exceed 230. What percent of balloons will
burst?
a. 16.67%
b. 20.33%
c. 79.67%
d. 83.37%
12. How many people in a group of 60 will have an IQ less than 92 if
their IQs are normally distributed with a mean of 100 and a standard
deviation of 15?
a. 18
b. 29
c. 30
d. 42
Short Answer
13. Calculate the z-score, to one decimal place, of x = 7.2 if 𝑥̅ = 8.1 and
𝜎 = 3.
14. Ravi’s math contest result put him in the 97-th percentile. If 4000
students competed, how many had a score higher than Ravi’s score?
Answers
Multiple Choice
1. B
7. D
2. A
8. C
3. B
9. D
4. C
10. D
5. C
11. B
6. A
12. A
Short Answer
13. The z-score is 0.3.
14. The number of students with a score higher than Ravi’s is 120.