Answer to Question #248808 in Statistics and Probability for Jamila

Question

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 5 miles. Find the probability of the following events:

A. The car travels more than 67 miles per gallon.

Probability =  

B. The car travels less than 53 miles per gallon. 

Probability =  

C. The car travels between 52 and 67 miles per gallon. 

Probability =  

Answer 1

N(60,25) = 60 + 5N(0,1)

So, the task is to calculate the next probabilities:

(a) P(60 + 5N(0,1) > 67) = P(N(0,1) > 1.4) = 0.0808

(b) P(60 + 5N(0,1) < 53) = P(60 + 5N(0,1) > 67) = 0.0808

(c) P(52 < 60 +5N(0,1) < 67) = P(-1.6 < N(0,1) < 1.4) = P(N(0,1) < 1.4) - P(N(0,1) < -1.6) = 0.9192 - 0.0548 = 0.8644