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 60 miles and a standard deviation of 5 miles. Find the probability of the following events:
Be sure to use at least 4 decimals of accuracy in your answers:

A) The car travels more than 65 miles per gallon.

B) The car travels between 53 and 64 miles per gallon.

Answer 1

Solution :

Given that ,

mean = = 60

standard deviation = = 5

P(x >65 ) = 1 - P(x<65 )

= 1 - P[(x -) / < (65 -60) /5 ]

= 1 - P(z < 1)

Using z table

= 1 - 0.8413

= 0.1587

probability= 0.1587

(B)

P(53< x <64 ) = P[(53 -60) /5 < (x - ) / < (64 -60) /5 )]

= P( -1.4< Z <0.8 )

= P(Z < 0.8) - P(Z <-1.4 )

Using z table   

= 0.7881 -0.0808

   probability= 0.7073