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 65 miles and a standard deviation of 7 miles. Find the probability of the following events: A. The car travels more than 70 miles per gallon. Probability = B. The car travels less than 60 miles per gallon. Probability = C. The car travels between 57 and 68 miles per gallon. Probability =

Answer 1

Solution :

Given that,

mean = $\mu$ = 65

standard deviation = $\sigma$ = 7

A ) P (x > 70 )

= 1 - P (x < 70 )

= 1 - P ( x -  $\mu$/ $\sigma$ ) < ( 70 - 65 / 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 < 60)

P ( x - $\mu$ / $\sigma$ ) < ( 60 - 65 / 7 )

P ( z < -5 / 7 )

P ( z < - 0.71)

= 0.2389

Probability = 0.2389

C ) P (57 < x < 68 )

P ( 57 - 65 / 7) < ( x -  $\mu$/ $\sigma$ ) < ( 68 - 65 / 7)

P ( - 8 / 7 < z < 3 / 7 )

P (-1.14 < z < 0.43)

P ( z < 0.43 ) - P ( z <-1.14)

Using z table

= 0.6664 - 0.1271

= 0.5393

Probability = 0.5393