Question

The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 24.8 miles per gallon, with a standard deviation of 6.2 miles per gallon. Assume that a Normal model applies. Find the probability that a randomly selected automobile will average:

1. Less than 20 miles per gallon.

2. More than 30 miles per gallon.

3. Between 25 and 32 miles per gallon

Answer 1

Solution :

Given that ,

mean = = 24.8

standard deviation = = 6.2

1) P(x < 20) = P((x - ) / < (20-24.8) / 6.2)

= P(z < -0.7742)

= 0.2194

Probability = 0.2194

2) P(x > 30) = 1 - P(x < 30)

= 1 - P((x - ) / < (30 - 24.8) / 6.2)

= 1 - P(z < 0.8387)

= 1 - 0.7992

= 0.2008

Probability = 0.2008

3) P(25 < x < 32) = P((25 - 24.8)/ 6.2) < (x - ) / < (32 - 24.8) / 6.2) )

= P(0.0323 < z < 1.1613)

= P(z < 1.1613) - P(z < 0.0323)

= 0.8772 - 0.5129

= 0.3643

Probability = 0.3643