Question

A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity for a randomly selected tank has a distribution that is approximately normal with the mean of 15 gallons and a standard deviation of 0.15 gallons. If 4 tanks are randomly selected, what is the probability that their average capacity will be between 14.75 and 16.10 gallons?

Please show work and explain, thank you.

Answer 1

For sampling distribution of mean with sample size n,

mean = 15 gallons

standrad deviation =

=

= 0.075

P( < A) = P(Z < (A - )/)

= P(14.75 < < 16.1)

= P( < 16.1) - P( < 14.75)

= P(Z < (16.1 - 15)/0.075) - P(Z < (14.75 - 15)/0.075)

= P(Z < 16.67) - P(Z < -3.33)

= 1 - 0.0004

= 0.9996