The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the g

Question

The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.2 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? (c) What proportion of hybrids gets between 58 and 61 miles per gallon? (d) What is the probability that a randomly selected hybrid gets less than 46 miles per gallon? Click the icon to view a table of areas under the normal curve. (a) The proportion of hybrids that gets over 62 miles per gallon is. (Round to four decimal places as needed.) (b) The proportion of hybrid that gets 50 miles per gallon or less is. (Round to four decimal places as needed.) (c) The proportion of hybrids that gets between 58 and 61 miles per gallon is (Round to four decimal places as needed.) (d) The probability that a randomly selected hybrid gets less than 46 miles per gallon is (Rou

Explanation / Answer

Mean = 56 miles per gallon

Standard deviation = 3.2 miles per gallon

a) P(X >62) = 1 - P(X < 62)

= 1 - P(Z < (62-56)/3.2)

= 1 - P(Z < 1.875)

= 1 - 0.9696

= 0.0304

b) P(X < 50) = P(Z < (50-56)/3.2)

=P(Z < -1.875)

= 0.0304

c) P(58 < X < 61) = P(X < 61) - P(X < 58)

= P(Z < (61 - 56)/3.2) - P(Z < (58 - 56)/3.2)

= P(Z < 1.56) - P(Z < 0.625)

= 0.9406 - 0.7341

= 0.2065

d) P(X < 46) = P(Z < (46-56)/3.2)

= P(Z < -3.125)

= 0.0009

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