Standard Normal Distribution 3.4
1. Find the area under the normal curve for a standard normal distribution for each of the following.
a. 0  z  1.32
b. 0  z  2.96
c. –1.18  z  0
d. 1.83  z  2.65
e. –0.31  z  1.56
f. z  1.6
g. z  –1.6
h. z  –1.23
2. In a normal distribution, find the probability of each of the following.
a. P(0  z  2)
b. P(0  z  0.84)
c. P(–1.30  z  1.75)
d. P(z  –1.0)
e. P(z  –2.26)
f. P(z  0.75)
4. For a standard normal distribution, find the probability of getting a z–value:
a. less than 1.9
b. greater than –1.57
c. less than 2.41
d. less than 0.33
e. between 1.29 and 2.56
f. between –2.03 and –1.06
g. between 1.75 and –0.08
h. less than –1.66 or greater than 0.81
5. z 
x

For a normal distribution with a mean of 33 and a standard deviation of 6, find the
z–score for each of the following values of x.
a. 31
b. 42
c. 25
d. 28
e. 38
f. 19
6. For a normal distribution, the mean is 12 and the standard deviation is 5. What is the probability,
to two decimal places, of having x if x lies in the interval, 8.2  x  10.8?
7. On average it takes 3 weeks to receive a package from China with a standard deviation of 5 days.
If the distribution is a normal distribution, then find the probability, in percent, that it will take the
package to come if it is:
a. less than 6 days
b. more than 26 days
c. between 16 and 31 days
8. z 
x

For each of the following z scores, where the mean is 21 and the standard
deviation is 4, determine the value of x.
a. –2.3
b. –0.5
c. 0
d. 1.9
e. 3.1
9. If the standard deviation of a normal distribution of a test is 8.78% and a score of 37% produces a
z–score of –1.69, then to the nearest 100th, the mean of this test is ____________.
10. On an English proficiency exam at the U of A, the mean score was 62% and the standard deviation
was 11. If Geoff’s z–score was 0.8, then what was his actual exam mark?
11. A candy company sells boxes of chocolates that have a mean of 44 chocolates and a standard
deviation of 2 chocolates.
a. What percent of the boxes contain at least 40 chocolates?
b. If the company produces 20 000 boxes a day, then how many have at least 40 chocolates?
c. How many boxes (of the 20 000) contain more than 47 chocolates?
12. A local company produces batteries with a mean life of 90 hours and a standard deviation of 3
hours.
a. What percent of the batteries last less than 87 hours?
b. What percent of the batteries last more than 99 hours?
c. What percent of the batteries last between 87 and 99 hours?
ANSWERS
1. a. 0.4066
e. 0.5623
b. 0.4985
f. 0.0548
c. 0.3810
g. 0.0548
d. 0.0296
h. 0.8907
2. a. 0.4772
e. 0.9881
b. 0.2995
f. 0.2266
c. 0.8631
d. 0.1587
4. a. 0.9713
e. 0.0933
b. 0.9418
f. 0.1234
c. 0.9920
g. 0.4918
d. 0.6293
h. 0.2575
5. a. –0.33
e. 0.83
b. 1.5
f. –2.33
c. –1.33
d. –0.83
7. a. 0.13%
b. 15.87%
c. 81.85%
8. a. 11.8
b. 19
c. 21
11. a. 97.73%
b. 19546
c. 1336
12. a. 15.87%
b. 0.13%
c. 84%
6. 0.18
9. 51.84%
10. 70.8
d. 28.6
e. 33.4