Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

190 CHAPTER 6 | Probability
6. Draw a vertical line through a normal distribution for
each of the following z-score locations. Determine
whether the body is on the right or left side of the line
and find the proportion in the body.
a. z = 2.50
b. z = 0.80
c. z = –0.50
d. z = –0.77
7. Find each of the following probabilities for a normal
distribution.
a. p(z > 1.25)
b. p(z > –0.60)
c. p(z < 0.70)
d. p(z < –1.30)
8. What proportion of a normal distribution is located
between each of the following z-score boundaries?
a. z = –0.25 and z = +0.25
b. z = –0.67 and z = +0.67
c. z = –1.20 and z = +1.20
9. Find each of the following probabilities for a normal
distribution.
a. p(–0.80 < z < 0.80)
b. p(–0.50 < z < 1.00)
c. p(0.20 < z < 1.50)
d. p(–1.20 < z < –0.80)
10. Find the z-score location of a vertical line that separates
a normal distribution as described in each of the
following.
a. 5% in the tail on the left
b. 30% in the tail on the right
c. 65% in the body on the left
d. 80% in the body on the right
11. Find the z-score boundaries that separate a normal
distribution as described in each of the following.
a. The middle 30% from the 70% in the tails.
b. The middle 40% from the 60% in the tails.
c. The middle 50% from the 50% in the tails.
d. The middle 60% from the 40% in the tails.
12. A normal distribution has a mean of μ = 70 and a
standard deviation of σ = 8. For each of the following
scores, indicate whether the tail is to the right or left
of the score and find the proportion of the distribution
located in the tail.
a. X = 72
b. X = 76
c. X = 66
d. X = 60
13. A normal distribution has a mean of μ = 30 and a
standard deviation of σ = 12. For each of the following
scores, indicate whether the body is to the right or
left of the score and find the proportion of the distribution
located in the body.
a. X = 33
b. X = 18
c. X = 24
d. X = 39
14. For a normal distribution with a mean of μ = 60 and
a standard deviation of σ = 10, find the proportion of
the population corresponding to each of the following.
a. Scores greater than 65.
b. Scores less than 68.
c. Scores between 50 and 70.
15. In 2014, the New York Yankees had a team batting
average of μ = 245 (actually 0.245 but we will avoid
the decimals). Of course, the batting average varies from
game to game, but assuming that the distribution of batting
averages for 162 games is normal with a standard
deviation is σ = 40 points, answer each of the following.
a. If you randomly select one game from 2014, what
is the probability that the team batting average was
over 300?
b. If you randomly select one game from 2014, what
is the probability that the team batting average was
under 200?
16. IQ test scores are standardized to produce a normal
distribution with a mean of μ = 100 and a standard
deviation of σ =15. Find the proportion of the population
in each of the following IQ categories.
a. Genius or near genius: IQ over 140
b. Very superior intelligence: IQ from 120–140
c. Average or normal intelligence: IQ from 90–109
17. The distribution of scores on the SAT is approximately
normal with a mean of μ = 500 and a standard
deviation of σ = 100. For the population of students
who have taken the SAT,
a. What proportion have SAT scores less than 400?
b. What proportion have SAT scores greater than
650?
c. What is the minimum SAT score needed to be in
the highest 20% of the population?
d. If the state college only accepts students from the
top 40% of the SAT distribution, what is the minimum
SAT score needed to be accepted?
18. According to a recent report, people smile an average
of μ = 62 time per day. Assuming that the distribution
of smiles is approximately normal with a standard
deviation of σ = 18, find each of the following values.
a. What proportion of people smile more than
80 times a day?
b. What proportion of people smile at least 50 times
a day?