4. Find the average retail gasoline price for regular grade gasoline sold in the United States on 5/11/2015 from the Department of Energy website at
https://www.eia.doe.gov/oil_gas/petroleum/data_publications/wrgp/mogas_home_page.html.
Assume the obtained price is the population mean price and the standard deviation is $0.63. Suppose a random sample of 55 gasoline stations will be selected, and a sample mean price per gallon will be computed for this sample data.
a. What are the mean and the standard deviation of the sample mean? What is the probability distribution for the sample mean? Describe this sampling distribution and draw the graph of this probability distribution with its mean and standard deviation.
b. What is the probability that the simple random sample will provide a sample mean more than $2.5?
c. What is the probability that the simple random sample will provide a sample mean less than $2.8?
5. Consider a population with a known population standard deviation of 13.2. In order to compute an interval estimate for the population mean, a sample of 64 observations is drawn. The sample mean is 37.6.
a. Compute the 90% confidence interval.
b. Compute the 95% confidence interval.
6. See Exercise 7.13 on page 299 of your textbook.
A personnel manager has found that historically the scores on aptitude tests given to applicants for entry-level positions follow a normal distribution with a standard deviation of 32.4 points. A random sample of nine test scores from the current group of applicants had a mean score of 187.9 points.
a. Find an 85% confidence interval for the population mean score of the current group of applicants.
b. Find an 95% confidence interval for the population mean score of the current group of applicants.