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Allegiant Airlines charges a mean base fare of $99. In addition, the airline charges for marking a
reservation on its website, checking bags, and inflight beverages. These additional charges average $31
per passenger (Bloomberg Businessweek, October 8-14, 2012). Suppose a random sample of 60
passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population
standard deviation of total flight cost is known to be $40.
What is the population mean cost per flight?
What is the probability the sample mean will be within $10 of the population mean cost per flight?
c. What is the probability the sample mean will be within $5 of the population mean cost per flight?
Fifteen percent of Australians smoke. By introducing tough laws banning brand labels on cigarette
packages, Australia hopes to reduce the percentage of people smoking to 10% by 2018 (Reuters website,
October 23,2012). Answer the following questions based on a sample of 240 Australians.
Show the sampling distribution of 𝑝̅, the proportion of Australians who are smokers.
What is the probability the sample proportion will be within ±0.04 of the population proportion?
c. What is the probability the sample proportion will be within ±0.02 of the population proportion?
The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke
(CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and
non-smokers uses a preliminary estimate of the proportion who smoke of 0.30.
How large a sample should be taken to estimate the proportion of smokers in the population with
a margin of error of 0.02? Use 95% confidence.
Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers.
What is the point estimate of the proportion of smokers in the population?
c. What is the 95% confidence interval for the proportion of smokers in the population?
Sales personnel for Skilling Distributors submit weekly reports listing the customer contacts made during
the week. A sample of 65 weekly reports showed an average of 20 customer contacts per week. The
sample standard deviation was 5. Provide 95% confidence interval for the population mean number of
weekly customer contacts for the sales personnel.
Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with a
margin of error of 1 mile per gallon is desired, how many automobiles should be used in the test? Assume
that preliminary mileage tests indicate the standard deviation is 3.6 miles per gallon.