Question

A new car that is a gas- and electric-powered hybrid has recently hit the market. The...

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 7 miles. Find the probability of the following events:

A. The car travels more than 65 miles per gallon. Probability =

B. The car travels less than 54 miles per gallon. Probability =

C. The car travels between 52 and 67 miles per gallon. Probability =

Solution :

Given that ,

mean = = 60

standard deviation = = 7

A)

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

= 1 - P((x - ) / < (65 - 60) / 7)

= 1 - P(z < 0.71)

= 1 - 0.7611 Using standard normal table.

= 0.2389

Probability = 0.2389

B)

P(x < 54) = P((x - ) / < (54 - 60) / 7)

= P(z < -0.86)

= 0.1949 Using standard normal table,

Probability = 0.1949

C)

P(52 < x < 67) = P((52 - 60)/ 7) < (x - ) /  < (67 - 60) / 7) )

= P(-1.14< z < 1)

= P(z < 1) - P(z < -1.14)

= 0.8413 - 0.1271

= 0.7142

Probability = 0.7142