36. In exercise 10, data on x  temperature rating (F) and y  price ($) for 11 sleeping bags manufactured by Bergans of Norway provided the estimated regression equation 

359.2668 5.2772x. For these data s  37.9372.

a. Develop a point estimate of the price for a sleeping bag with a temperature rating of 30.

b. Develop a 95% confidence interval for the mean overall temperature rating for all sleeping bags with a temperature rating of 30.

c. Suppose that Bergans developed a new model with a temperature rating of 30. Develop a 95% prediction interval for the price of this new model.

d. Discuss the differences in your answers to parts

(b) and (c).