Name: ____________________________________
Show enough work so that your method can be followed: all
calculations for z, appropriate shaded area.
1. The scores on the Wechsler Adult Intelligence Scale for 20- to
34-years-olds are, approximately, normally distributed with
mean 100 and standard deviation 20.
a. What percentage of 20- to 34-year-olds are between the
intelligence scores of 80 and 120.
1a. ____________________
b. What percentage of adults have an IQ score less than 65.
1b. ____________________
c. What percentage of adults have an IQ greater than 125.
1c. ____________________
Find the percentage of the given z-score.
2. z is less than -1.57
3. z is greater than 1.07
4. z is between -2.51 and 3.22
5. z is between -1.32 and 1.51
6. According to a survey conducted by television advertisers, the
average adult American watches an average of 7.58 hours of
television per day. The data is normally distributed with a
standard deviation of 2.80 hours. Find the probability that a
randomly selected person watches less than 5.00 hours of
television in a day.
2. ____________________
3. ____________________
4. ____________________
5. ____________________
6. ____________________
7. The heights of the 1280 students at East Meck High School are
normally distributed with a mean of 70 inches and a standard
deviation of 1.5 inches
a. Draw and label the normal curve.
b. 68% of the students fall between what two heights?
7b. ____________________
c. What percent of the students are between 55.5 and 73 inches
tall?
7c. ____________________
d. Approximately how many students are more than 71.5 inches
tall?
7d. ____________________
e. If a student is 64 inches tall, how many standard deviations from
the mean are they?
7e. ____________________
f. If a student is 74 inches tall, how many standard deviations from
the mean are they?
7f. ____________________
g. If you pick a student at random, what is the probability that they
will be between 64 and 74 inches tall?
7g. ____________________
h. If you pick a student at random, what is the probability they will
be between 65.5 and 74.5 inches tall?
7h. ____________________
i. What is the probability they will be more than 70 inches tall?
7i. ____________________
j. What is the probability they will be less than 63 inches tall?
7j. ____________________
8. Insurance companies have determined that US males between
the ages of 16 and 24, drive an average of 11,218 miles each
year with a standard deviation of 3963 miles. Assume the data
is normally distributed. For a randomly selected male in that
age group, find the probability that he drives less than 12,000
miles per year.
8. ____________________
9. The heights of six-year old girls are normally distributed with a
mean of 117.80 cm and a standard deviation of 3.52 cm. Find
the probability that a randomly selected six-year girl has a height
between 117.80 cm and 120.56 cm.
9. ____________________
10. The average heating bill for a residential area is $113 for the
month of November with a standard deviation of $8. If the
amounts of the heating bills are normally distributed, find the
probability that the average bill for a randomly selected resident
is more than $125.
11. The average adult spends 4 hours per week on a home computer,
with a standard deviation of 2 hour. What percent of adults
spend less than 6 hours per week on their home computer?
10. ____________________
11. ____________________
12. The average weight of an 8 week old male golden retriever is
9.23 lbs. The standard deviation of this weight being 5 lbs.
a. What percent of the puppies weigh more than 10.5 lbs?
12a. ____________________
b. What percent of puppies’ weights fall between 8.75 and 15.8
lbs?
12b. ____________________
13. Find Z if X = 24, x = 25, and σ = 1.8.
14. A light bulb advertises that its average (mean) life is 350 hours,
with a standard deviation of 20 hours.
a. What is the probability that the light bulb will last less than 295
hours?
13. ____________________
14a. ____________________
b. What is the probability that the light bulb will last more than 375
hours?
14b. ____________________
c. What is the probability that the light bulb will last between 285
and 365 hours?
14c. ____________________
15. Draw an example of a normal distribution:
16. What are two methods of assessing normality?
16._______________________
__________________________
__________________________
__________________________
IQ scores for a random sample of people are shown below.
72 79 87 91 99 101 103 106 111 113 116 126
17._______________________
__________________________
17. Is the above data normal or skewed? Why?
__________________________
__________________________
18. Students who score in the top 15% on a mathematics admission test
at Greenville Tech place out of taking a college math class. If the
average score is 80 with a standard deviation of 6, what is the score that
determines if a student does or does not have to take a college math
course?
19. John finds that there is a scholarship available to all persons scoring
in the top 10% on the ACT test. If the mean score on the ACT is 23
with a standard deviation of 3.7, what score does he need in order to
qualify for the scholarship?
18. ____________________
19. ____________________
20. Use the z-score table to find the value of z is less than -0.56.
a) 35.57%
b) 64.43%
c) 28.77%
d) 0.71%
20. ____________________
21. Use the z-score table to find the value of z is greater than 1.27.
21. ____________________
a) 5.71%
b) 94.29%
c) 82.38%
d) 10.2%