37. Manufacturer Claims You work for a consumer watchdog publication and are testing the advertising claims of a tire manufacturer. The manufacturer claims that the life spans of the tires are normally distributed, with a mean of 40,000 miles and a standard deviation of 4000 miles. You test 16 tires and get the following life spans.
48,778 41,046 29,083 36,394 32,302 42,787 41,972 37,229
25,314 31,920 38,030 38,445 30,750 38,886 36,770 46,049
(a) Draw a frequency histogram to display these data. Use five classes. Is it reasonable to assume that the life spans are normally distributed? Why?
(b) Find the mean and standard deviation of your sample.
(c) Compare the mean and standard deviation of your sample with those in the manufacturer’s claim. Discuss the differences.