Question

A gasoline tank for a Honda Accord is engineered to hold 15 gallons of gas.  Gas tank capacity for a randomly selected Accord has an approximately normal distribution with mean 15.0 gallons and standard deviation of 0.1 gallons.

(a) What is the probability that a randomly selected Accord has a gas tank capacity within one standard deviation of the mean?

(b) What is the probability that a randomly selected tank will hold at most 14.85 gallons? Sketch a graph of this situation and shade the appropriate region.

(c) What is the probability that in the next twelve cars randomly selected, exactly four of those tanks will hold at most 14.85 gallons? Use your results from part (b).

Answer 1

a)

Let X denote the capacity for the tank (in gallons). Then

Required probability =

b)

Required probability =

c)

Let Y denote the number of cars in the sample that hold at most 14.85 gallons.

Then

Required probability =