Question

1) The Environmental Protection Agency (EPA) rates the mean highway gas mileage of the 2013 Ford Edge to be 27 miles per gallon. Assume the standard deviation is 3 miles per gallon. A rental car company buys 60 of these cars. What is the probability that the average mileage of the fleet (sample mean) is greater than 26.5 miles per gallon?

2) The Internal Revenue Service reports that the mean federal income tax paid in a recent year was $8040. Assume that the standard deviation is $5000. The IRS plans to draw a sample of 1000 tax returns to study the effect of a new tax law. What is the probability that the sample mean tax is between $7600 and $7900?

3) A sample of 314 patients between the ages of 38 and 82 were given a combination of the drugs ezetimibe and simvastatin. They achieved a mean reduction in total cholesterol of 0.94 millimole per liter. Assume the population standard deviation is 0.18. Construct a 90% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drugs.

4) The lifetime of a certain type of battery is known to be normally distributed with population standard deviation 20 hours. A sample of 15 batteries had a mean lifetime of 120.1 hours. Construct a 95% confidence interval for the mean lifetime for this type of battery.

Answer 1