1. In a recent year, the scores for the reading portion of a test were normally distributed, with a
mean of 21.8 and a standard deviation of 5.3. Complete parts a through d below.
a. Find the probability that a randomly selected high school student who took the reading
portion of the test has a score that is less than 20.
The probability of a student scoring less than 20 is _____ (round to four decimal places as
needed)
b. Find the probability that a randomly selected high school student who took the reading
portion of the test has a score that is between 15.0 and 28.6
The probability of a student scoring between 15.0 and 28.6 is ______ (round to four
decimal places as needed)
c. Find the probability that a randomly selected high school student who took the reading
portion of the test has a score that is more than 32.6
The probability of a student scoring more than 32.6 is _____ (round to four decimal
places as needed)
d. Identify any unusual events. Explain your reasoning. Choose the correct answer below A. None of the events are unusual because all the probabilities are greater than
0.05 B. The event in part c is unusual because its probability is less than 0.05 C. The event in part a is unusual because its probability is less than 0.05 D. The events in part a and b are unusual because its probabilities are less than
0.05
2. Use the normal distribution of SAT critical reading scores for which the mean is 513 and the
standard deviation is 118. Assume the variable x is normally distributed
a. What percent of the SAT verbal scores are less than 550
b. If 1000 SAT verbal scores are randomly selected, about how many would you expect to
be greater than 525?
a. Approximately ___% of the SAT verbal scores are less than 550 (round to two decimal places
as needed).
b. You would expect that approximately ___ SAT verbal scores would be greater than 525.
(round to the nearest whole number as needed)
3. The table shows the results of a survey in which separate samples of 400 adults each from the
East, South, Midwest and West were asked if traffic congestion is a serious problem in their
community. Complete parts a and b
TABLE
BAD TRAFFIC CONGESTION?: Adults who say that traffic congestion is a serious problem
East 36% South 31% Midwest 27%
West
a. 57%
Construct a 95% confidence interval for the proportion of adults from West who say traffic
congestion is a serious problem.
The 95% confidence interval for the proportion of adults from the west who say traffic
congestion is a serious problem is ___ ____ (round to three decimal places as needed) b. Construct a 95% confidence interval for the proportion of the adults from the Midwest who say
traffic congestion is a serious problem.
The 95% confidence interval for the proportion of adults from the Midwest who say traffic
congestion is a serious problem is ___ ___ (round to three decimal places as needed) 4. In a random sample of 35 refrigerators, the mean repair cost was $128.00 and the population
standard deviation is $15.80. Construct a 95% confidence interval for the population mean
repair cost. Interpret the results.
Construct a 95% confidence interval for the population mean repair cost.
The 95% confidence interval is __ __ (round to two decimal places as needed)
Interpret your results. Choose the correct answer below. A. The confidence interval contains 95% of the mean repair costs
B. With 95% confidence, it can be said that the confidence interval contains the true
mean repair cost.
C. With 96% confidence, it can be said that the confidence interval contains the sample
mean repair cost. 5. Find the probability and interpret the results. If convenient, use technology to find the
probability.
The population mean annual salary for environmental compliance specialist is about $60,000. A
random sample of 37 specialists is drawn from this population. What is the probability that the
mean salary of the sample is less than $57,500? Assume “a”=$6,400
The probability that the mean salary of the sample is less than $57,500 is ______ (round to four
decimal places as needed)
Interpret the results. Choose the correct answer below. A. About 0.87% of samples of 37 specialists will have a mean salary less than $57,500.
This is not an unusual event. B. About 87% of samples of 37 specialists will have a mean salary less than $57,500. This
is not an unusual event. C. Only 87% of samples of 37 specialists will have a mean salary less than $57,500. This
is an unusual event.
D. Only 0.87% of samples of 37 specialists will have a mean salary less than $57,500.
This is unusual event. 6. A researcher wishes to estimate with 90% confidence, the population of adults who think the
president of their country can control the price of gasoline. Her estimate must be accurate
within 1% of the true proportion.
a. No preliminary estimate is available. Find the minimum sample size needed.
b. Find the minimum sample size needed, using a prior study that found that 42% of the
respondents said they think their president can control the price of gasoline.
c. Compare the results from parts a and b
a) What is the minimum sample size needed assuming that no prior information
is available? n= ________ (round to the nearest whole number as needed)
b) What is the minimum sample size needed using a prior study that found that
42% of the respondents said they think their president can control the price of
gasoline? n= _____ (round up to the nearest whole number as needed).
c) How do the results from a and b compare?
o A. Having an estimate of the population proportion reduce the
minimum sample size needed.
o B. Having an estimate of the population proportion raises the
minimum sample size needed.
o Having an estimate of the population proportion has no effect on the
minimum sample size as needed. 7. Assume the random variable x is normally distributed with mean u=89 and standard deviation
a=4. Find the indicated probability.
P(x<83)
P(x<83) = ______ (round to four decimal places as needed). 8. Construct the confidence interval for the population mean u.
c= 0.90, x – = 15.2, a=4.0, and n = 100
A 90% confidence interval for u is __ __. (round to one decimal place as needed). 9. In a survey of 3353 adults, 1415 say they have started paying bills online in the last year.
Construct a 99% confidence interval for the population proportion. Interpret the results.
A 99% confidence interval for the population proportion is __ __. (round to three decimal places
as needed). Interpret your results. Choose the correct answer below.
o A. With 99% confidence, it can be said that the population proportion of adults who say
they have started paying bills online in the last year is between the endpoints of the
given confidence interval.
o B. The endpoints of the given confidence interval show that adults pay bills online 99%
of the time.
o C. With 99% confidence, it can be said that the sample proportion of adults who say
they have started paying bills online in the last year is between the endpoints of the
given confidence interval.