Question

A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 45 miles and a standard deviation of 7 miles. Find the probability of the following events:

A. The car travels more than 53 miles per gallon.

Probability =  

B. The car travels less than 42 miles per gallon.

Probability =  

C. The car travels between 39 and 52 miles per gallon.

Probability =

Answer 1

Solution :

Given ,

mean = = 45

standard deviation = = 7

P(x > 53) = 1 - P(x< 53)

= 1 - P[(x -) / < (53 -45) /7 ]

= 1 - P(z <1.14 )

Using z table

= 1 - 0.8729

= 0.1271

probability=0.1271

(b)

P(X< 42 ) = P[(X- ) / < ( 42 -45) /7 ]

= P(z <-0.43 )

Using z table

= 0.3336

probability=0.3336

(c)

P(39< x <52 ) = P[(39 -45) /7 < (x - ) / < (52-45) /7 )]

= P( -0.86< Z <1 )

= P(Z < 1) - P(Z < -0.86)

Using z table   

= 0.8413-0.1949

probability= 0.6464