Problem #2 (12 points) An automobile manufacturer introduces a new model that av

Question

Problem #2 (12 points) An automobile manufacturer introduces a new model that averages 27 miles per allon in the city under normal conditions. Assume that in-city mileage for this model is approximately normally distributed with standard deviation of 2.5 miles per gallon. What is the probability that a person who will purchase this model, will end up with a car that averages between 25 and 29 miles per gallon for in-city driving? a. (5 points) 2. 632 b. Find the value of the 90th percentile, Pso, for this random variable. (5 points) c. Use information from part (b) to circle the correct choice and to fill in the blanks in the following sentence: 2 points) )miles per gallon for in-city driving.

Explanation / Answer

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 27 miles per gallon

Standard deviation = 2.5 miles per gallon

a) P(averages between 25 and 29 miles per gallon) = P(X < 29) - P(X < 25)

= P(Z < (29-27)/2.5) - P(Z < (25-27/2.5)

= P(Z < 0.8) - P(Z < -0.8)

= 0.7881 - 0.2119

= 0.5762

b) P(X < P90) = 0.90

P(Z < (P90 - 27)/2.5) = 0.90

(P90 - 27)/2.5 = 1.28

P90 = 30.2 miles per gallon

c) 90% of the new model cars average at most 30.2 miles per gallon for in-city driving

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