The mean gas mileage for a hybrid car is 57 miles per gallon. Suppose that the g

Question

The mean gas mileage for a hybrid car is 57 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.5 miles per gallon. (a) What proportion of hybrids gets over 62 miles per gallon? (b) What proportion of hybrids gets 50 miles per gallon or less? left parenthesis c right parenthesis What proportion of hybrids gets between 57 and 62 miles per gallon? (d) What is the probability that a randomly selected hybrid gets less than 45 miles per gallon?

Explanation / Answer

= 57 = 3.5

Z = (X - ) /

(a) X >= 62

Z = (62 - 57) / 3.5

= 1.4286

Probability from z tables (right tailed) = 0.0766.

(b) X <= 50

Z = (50 - 57) / 3.5

= -2

Probability from z tables = 0.0228.

(c) Proportion between 57 and 62 = (1 - 0.0766) - 0.0288 = 0.8946.

(d) X < 45

Z = (45- 57) / 3.5

= -3.4286

Probability from z tables = 0.0003.

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