A gasoline tank for a certain car is designed to hold 15 gal

A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons.

(a) Themanufacturerofthisgasolinetankconsidersthelargest2%ofthesetankstoolarge to put on the market. How large does a tank have to be, to be considered too large?

(b) What proportion of tanks will hold between 14.75 and 15.10 gallons of gas?

(c) If a simple random sample of four tanks is selected, and their capacities can be con- sidered independent, what is the probability that all four will hold between 14.75 and 15.10 gallons of gas?

(d) If four tanks are randomly selected, what is the probability that their average capacity will be between 14.75 and 15.10 gallons?

Solution