Problem Set 7
1. As part of a marketing study, the Food King Supermarket chain has randomly sampled 150 customers. The average dollar volume purchased by the customers in this sample was $84.14, that is, the sample mean from a sample of size 150 was $84.14.
Before sampling, the company assumed that the population distribution of customer purchases had a mean of $80.00 and a standard deviation of $12.00.
If their assumption is correct regarding the population mean and standard deviation, what is the probability of observing a sample mean of $84.14 or greater?
2. An automatic saw at a local lumber mill cuts 2-by-4s to an average length of 121 inches. Because the saw is a mechanical device, not all the boards are 121 inches long. In fact, the distribution of lengths has a variance of 0.16.
a) The 2x4s are sold as being 10 feet in length (120 inches). What is the proportion of boards cut by this process that are less than the advertised length?
b) The saw operator took a sample of 36 boards. If the saw is set correctly, what is the probability the average length of the sample boards is more than 120.9 inches?
c) What should the saw operator conclude if she finds the sample to have an average length greater than 121.2 inches?
3. A sample of 500 business professionals found that 30% chose an airline based on price.
a) If the population proportion of all business professionals who select an airline based on price is 0.27, then what is the probability that we would find a sample proportion of 0.30 or more in a sample of 500?
b) If the population proportion of all business professionals who select an airline based on price is 0.29, then what is the probability that we would find a sample proportion of 0.30 or more in a sample of 500?