STA 2023 Statistics – Test 4
Due: 6/7/2022
Please read the instructions before you get started.
Instructions:
1. Round all answers to four decimal places, as necessary, unless otherwise indicated.
2. Show all work. Answer only will receive half credit. Indicate function used on calculator and
what was entered.
3. Do your work on a separate sheet of paper (or create more space between problems).
1) The number of violent crimes committed in a day in a particular city has a distribution with a mean
of 2.6 crimes per day and a standard deviation of 5 crimes per day. A random sample of 64 days
was observed, and the mean number of crimes for the sample was calculated. Describe the
sampling distribution of x , the sample mean. Round the standard deviation to four decimal places.
2) According to a study conducted in one city, 29% of adults in the city have credit card debts of more
than $2000. A simple random sample of n = 450 adults is obtained from the city. Describe the
sampling distribution of p̂ , the sample proportion of adults who have credit card debts of more
than $2000. Round the standard deviation to four decimal places.
3) Assume that blood pressure readings are normally distributed with a mean of 115 and a standard
deviation of 4.8. If 125 people are randomly selected, find the probability that their mean blood
pressure will be less than 117.
4) The National Association of Realtors estimates that 22% of all homes purchased in 2004 were
considered investment properties. If a sample of 600 homes sold in 2004 is obtained what is the
probability that at least 150 homes are going to be used as investment property?
5) Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard
welds that for the afternoon shift 6.5% of all welds done will be substandard. If Smith checks a
sample of 350 of the welds completed that shift, what is the probability that he will find between
5% and 8% substandard welds?
6) Assume that the heights of women are normally distributed with a mean of 63.6 inches and a
standard deviation of 2.5 inches. A particular project requires that the heights of women be between
65 and 70 inches.
a. What is the probability that a randomly selected woman will have a height between 65 and
79 inches?
b. If 25 women are randomly selected, what is the probability that their mean height is
between 65 and 70 inches?
7) According to a Gallup poll, 82% of Americans are satisfied with the way their lives are going.
Would it be unusual for a survey of 110 Americans to reveal that fewer than 80 are satisfied with
the direction of their lives?
8) The sampling distribution of the sample mean is shown.
a) What is  x ?
b) What is  x ?
c) If the sample size is n = 12, what is likely true about the shape of the population?
d) If the sample size is n = 12, what is the standard deviation of the population from which the
sample was drawn? Round to the nearest thousandth where appropriate.
9) An insurance adjustment director is studying if people are padding their insurance claim to cover
their deductible. They currently have 40 claims they are looking into. To say that the distribution of
p̂ , the sample proportion of adults who pad their insurance claim, is approximately normal, how
many more claims do they need to sample if is known that 12% of adults pad their insurance
claims? Use the fact that to be approximately normal, 𝑛𝑝(1 − 𝑝) ≥ 10. Remember to round up.
10) The reading speed of second-grade students is approximately normal, with a mean of 90 words per
minute (wpm) and a standard deviation of 10 wpm.
a. What is the probability that a random sample of 25 second-grade students results in a mean
reading rate of more than 97 words per minute?
b. There is a 5% chance that the mean reading speed of a random sample of 20 second-grade
students will exceed what value?