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 42 and 53 miles per gallon. Probability =

Answer 1

Solution :

Given that,

mean = = 50

standard deviation = = 8

a ) P (x > 55 )

= 1 - P (x < 55 )

= 1 - P ( x -  / ) < ( 55 - 50 / 8)

= 1 - P ( z < 5 / 8 )

= 1 - P ( z < -1.704)

Using z table

= 1 - 0.0.7324

= 0.2676

Probability = 0.2676

b ) P( x <47 )

P ( x - / ) < ( 47 - 50 / 8 )

P ( z < - 3 / 8 )

P ( z < - 0.37)

= 0.3557

Probability = 0.3557

c ) P (42 < x < 53 )

P ( 42 - 50 / 8 ) < ( x -  / ) < ( 53 - 50 / 8 )

P ( - 8 / 8 < z < 3 / 8 )

P (-1 < z < -0.37 )

P ( z < 0.37 ) - P ( z < -1)

Using z table

= 0.6443 - 0.1587

= 0.4857

Probability = 0.4857