Download Chapter 9 Review #1 - Rochester Community Schools

A.P. Statistics Chapter 9 Review #1
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In Exercises 1-8, assume that women’s heights are normally distributed with a mean given by μ= 63.6 in. and a
standard deviation given by σ = 2.5 in.
1.) If 1 woman is randomly selected, find the probability that her height is between 63.6 in. and 64.6 in.
2.) If 36 women are randomly selected, find the probability that they have a mean height between 63.6 in and
64.6 in.
3.) If 1 woman is randomly selected, find the probability that her height is above 63.0 in.
4.) If 100 women are randomly selected, find the probability that they have a mean height greater than 63.0 in.
5.) If 1 woman is randomly selected, find the probability that her height is above 64.0 in.
6.) If 50 women are randomly selected, find the probability that they have a mean height greater than 64.0 in.
7.) If 1 woman is randomly selected, find the probability that her height is between 63.0 in and 65.0 in.
8.) If 75 women are randomly selected, find the probability that they have a mean height between 63.0 in and
65.0 in.
9.) Replacement times for CD players are normally distributed with a mean of 7.1 years and a standard
deviation of 1.4 years. Find the probability that 45 randomly selected CD players will have a mean
replacement time greater than 7.0 years.
10.) According to the Opinion Research Corporation, men spend an average of 11.4 min in the shower.
Assume that the times are normally distributed with a standard deviation of 1.8 min. If 33 men are
randomly selected, find the probability that their shower times have a mean between 11.0 min and
12.0 min.
11.) The annual precipitation amounts for Iowa appear to e normally distributed with a mean of 32.473 in. and
a standard deviation of 5.601 in.
a.) If one year is randomly selected, find the probability that the annual precipitation is less
than 29.000 in.
b.) If a decade of ten years is randomly selected, find the probability that the annual precipitation
amounts have a mean less than 29.000 in.
c.) Given that part (b) involves a sample size that is not larger than 30, why can the central limit
theorem be used?
12.) The ages of U.S. commercial aircrafts have a mean of 13.0 years and a standard deviation of 7.9 years. If
the Federal Aviation Administration randomly selects 3 commercial aircrafts for special stress tests, find
the probability that the mean age of this sample group is greater than 15.0 years.
13.) The town of Newport operates a rubbish waste disposal facility that is overloaded if its 4872 households
have total weights with a mean that exceeds 27.88 lbs. in a week. The total weights are normally
distributed with a mean of 27.44 lbs. and a standard deviation of 12.46 lbs. What is the proportion of
weeks in which the waste disposal facility is overloaded? Is this an acceptable level, or should action be
taken to correct a problem of an overloaded system?
14.) SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120.
Randomly selected ACT verbal scores are obtained from the population of students who took a test
preparatory course from the Tillman Training School. Assume that this training course has no effect on
test scores.
a.) If 1 of the students is randomly selected, find the probability that he or she obtained a score greater
than 440.
b.) If 100 students are randomly selected, find the probability that their mean score is greater than 440.
c.) If 1000 Tillman students achieve a sample mean of 40, does it seem reasonable to conclude that the
course is effective because the students perform better on the SAT?
15.) The lengths of pregnancies are normally distrusted with a mean of 268 days and a standard deviation of 1
days.
a.) If 1 pregnant woman is randomly selected, find the probability that her length of pregnancy is less
than 260 days.
b.) If 25 randomly selected women are put on a special diet just before they become pregnant, find the
probability that their lengths of pregnancy have a mean that is less than 260 days (assuming that the
diet has no effect).
c.) If the 2 women do have a mean that is less than 260 days, should the medical supervisors be
concerned?
16.) Using a standard measure of satisfaction with salaries, a study finds that college administrators have a
mean of 38.9 and a standard deviation of 12.4. A pollster randomly selects 150 college administrators and
measures their levels of satisfaction with their salaries.
a.) Find the probability that the mean is greater than 42.0.
b.) If a sample of 150 college administrators does yield a mean of 42.0 or greater, is their reason to
believe that this sample came from a population with a mean that is higher than 38.9?