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 45 miles and a standard deviation of 7 miles. Find the probability of the following events:

A. The car travels more than 50 miles per gallon.

Probability =

B. The car travels less than 40 miles per gallon.

Probability =

C. The car travels between 37 and 51 miles per gallon.

Probability =

Answer 1

Solution :

Given that,

mean = = 45

standard deviation = = 7

a ) P (x > 50 )

= 1 - P (x < 50 )

= 1 - P ( x -  / ) < ( 50 - 45 / 7)

= 1 - P ( z < 5 / 7 )

= 1 - P ( z < 0.71)

Using z table

= 1 - 0.7611

= 0.2389

Probability =0.2389

b ) P( x < 40 )

P ( x - / ) < ( 40 - 45 / 7)

P ( z < -5 / 7 )

P ( z < -0.71)

= 0.2389

Probability = 0.2389

c ) P (37 < x < 51 )

P ( 37 - 45 / 7) < ( x -  / ) < ( 51 - 45 / 7)

P ( - 8 / 7 < z < 6 / 7 )

P (-1.14 < z < 0.86 )

P ( z < 0.86 ) - P ( z < -1.14)

Using z table

= 0.8051 - 0.1271

= 0.6780

Probability = 0.6780