A simple random sample of 20 new automobile models yielded the data shown to the right on fuel tank capacity, in gallons. 15.1 16.5 22.9 16.7 18.9 21.6 20.7 16.2 18.8 20.2 15.9 21.8 16.6 22.9 22.7 20.8 16.2 21.6 17.6 21.8

a. Find a point estimate for the mean fuel tank capacity for all new automobile models.

(Note: xi = 385.5 gallons.)

b. Determine a 95.44% confidence interval for the mean fuel tank capacity of all new automobile models. Assume σ = 3.40 gallons.

c. How would you decide whether fuel tank capacities for new automobile models are approximately normally distributed?

d. Must fuel tank capacities for new automobile models be exactly normally distributed for the confidence interval that you obtained in part

(b) to be approximately correct? Explain your answer.