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.