Answer to Question #249201 in Statistics and Probability for yara

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 50 miles and a standard deviation of 8 miles. Find the probability of the following events:

A. The car travels more than 55 miles per gallon.

Probability = 

B. The car travels less than 47 miles per gallon.

Probability = 

C. The car travels between 47 and 58 miles per gallon.

Probability = 

Answer 1

A.

$P(X > 55) = 1 - P[z > \frac{55-50}{8}] = 1-P(z > 0.625)$

$P(X > 55) = 1-0.734$

Probability = 0.266 or 26.6%

There is 26.6% probability that car travels more than 55 miles per gallon.

B.

$P(X < 47) = P[z < \frac{47-50}{8}] = P(z < -0.375)$

$P(X < 47) =0.354$

Probability = 0.354 or 35.4%

This means there is 35.4% probability that car travels less than 47 miles per gallon.

C.

$P(47 < X < 58) = P[\frac{47-50}{8}<z<\frac{58-50}{8}] = P(-0.375<z<1)$

$=P(z<1) - P(z<-0.375)$

Probability = 0.841 - 0.354 = 0.488

It is found that there is 48.8% chance of the car travels between 47 and 58 miles per gallon.