Download Review Section 5.1 Use the Standard Normal Table to find the

Review
Section 5.1
Use the Standard Normal Table to find the indicated area under the standard normal
curve.
1. To the left of z = .33
2. To the left of z = −.027
3. To the right of 𝑧 = 1.68
4. To the right of z = 0.12
5. Between z = -1.55 and z = 1.04
6. Between z = -1.96 and z = 1.96
7. To the left of z = -1.5 and to the right of z = 1.5
Section 5.2
Find the indicated probabilities.
8. P (z < 1.28)
9. P (z > -0.74)
10. P (-2.15 < z < 1.55
11. P (z < -2.50 or z > 2.50)
12. A study found that the mean migration distance of the green turtle was 2200 kilometers
and the standard deviation was 625 kilometers. Assuming that the distances are normally
distributed, find the probability that a randomly selected green turtle migrates a distance
of
(a) Less than 1900 kilometers.
(b) Between 2000 kilometers and 2500 kilometers.
(c) Greater than 2450 kilometers.
Section 5.3
Use the Standard Normal Table to find the z-score that corresponds to the given cumulative area
or percentile.
13. 0.4721
14. 0.1
15. 0.8708
16. P85
17. P20
In Exercises18–22, use the following information. On a dry surface, the braking distance (in
meters) of a Ford Expedition can be approximated by a normal distribution, as shown in the
graph.
18. Find the braking distance of a Ford Expedition that corresponds to z = -2.4.
19. Find the braking distance of a Ford Expedition that corresponds to z = 1.2
20. What braking distance of a Ford Expedition represents the 95th percentile?
21. What is the shortest braking distance of a Ford Expedition that can be in the top 10% of
braking distances?
22. What is the longest braking distance of a Ford Expedition that can be in the bottom 5% of
braking distances?
Section 5.4
Use the Central Limit Theorem to find the mean and standard error of the mean of the
indicated sampling distribution.
23. The consumption of processed fruits by people in the United States in a recent year was
normally distributed, with a mean of 144.3 pounds and a standard deviation of 51.6 pounds.
Random samples of size 35 are drawn from this population.
24. The consumption of processed vegetables by people in the United States in a recent year was
normally distributed, with a mean of 218.2 pounds and a standard deviation of 68.1 pounds.
Random samples of size 40 are drawn from this population.
Find the probabilities for the sampling distributions.
25. The mean annual salary for chauffeurs is $29,200. A random sample of size 45 is drawn from
this population. What is the probability that the mean annual salary is (a) less than $29,000 and
(b) more than $31,000? Assume σ = $1500
26. The mean value of land and buildings per acre for farms is $1300. A random sample of size
36 is drawn. What is the probability that the mean value of land and buildings per acre is (a) less
than $1400 and (b) more than $1150? Assume σ = $250.
27. The mean price of houses in a city is $1.5 million with a standard deviation of $500,000. The
house prices are normally distributed. You randomly select 15 houses in this city. What is the
probability that the mean price will be less than $1.125 million?
28. Mean rent in a city is $500 per month with a standard deviation of $30. The rents are
normally distributed. You randomly select 15 apartments in this city. What is the probability that
the mean price will be more than $525?
Section 5.5
Decide whether you can use the normal distribution to approximate the binomial
distribution. If you can, find the mean and standard deviation.
29. In a recent year, the American Cancer Society said that the five-year survival rate for new
cases of stage 1 kidney cancer is 95%. You randomly select 12 men who were new stage 1
kidney cancer cases this year and calculate their five-year survival rate.
30. A survey indicates that 59% of men purchased perfume in the past year. You randomly select
15 men and ask them if they have purchased perfume in the past year.
31. Seventy percent of children ages 12 to 17 keep at least part of their savings in a savings
account. You randomly select 45 children and ask each if he or she keeps at least part of his or
her savings in a savings account. Find the probability that at most 20 children will say yes.