Question

A new car that is a gas- and electric-powered hybrid has recently hit the market. The...

A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 60 miles and a standard deviation of 6 miles. Find the probability of the following events:

A. The car travels more than 63 miles per gallon.

Probability =

B. The car travels less than 52 miles per gallon.

Probability =

C. The car travels between 52 and 66 miles per gallon.

Probability =

Homework Answers

Answer #1

Solution :

A.

P(x > 63) = 1 - P(x < 63)

= 1 - P[(x - ) / < (63 - 60) / 6)

= 1 - P(z < 0.5)

= 1 - 0.6915

= 0.3085

Probability = 0.3085

B.

P(x < 52) = P[(x - ) / < (52 - 60) / 6]

= P(z < -1.33)

= 0.0918

Probability = 0.0918

C.

P(52 < x < 66) = P[(52 - 60)/ 6) < (x - ) /  < (66 - 60) / 6) ]

= P(-1.33 < z < 1)

= P(z < 1) - P(z < -1.33)

= 0.8413 - 0.0918

= 0.7495

Probability = 0.7495

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