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 7 miles. Find the probability of the following events:

A. The car travels more than 53 miles per gallon.

Probability =

B. The car travels less than 47 miles per gallon.

Probability =

C. The car travels between 42 and 58 miles per gallon.

Probability =

Answer 1

Solution :

Given that ,

A.

P(x >53 ) = 1 - P(x < 53)

= 1 - P[(x - ) / < (53 - 50) / 7)

= 1 - P(z < 0.4286)

= 1 - 0.6659

= 0.3341

Probability = 0.3341

B.

P(x < 47) = P[(x - ) / < (47 - 50) / 7]

= P(z < -0.4286)

= 0.3341

Probability = 0.3341

C.

P(42 < x < 58) = P[(42 - 50)/ 7) < (x - ) /  < (58 - 50) / 7) ]

= P(-1.1429 < z < 1.1429)

= P(z < 1.1429) - P(z < -1.1429)

= 0.8735 - 0.1265

= 0.747

Probability = 0.747