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Elementary Statistics Departmental Final Exam Part l Form B) Empllo Problem #2 (12 points) An automobile manufacturer introduces a new model that averages 28 miles per gallon in the city under normal conditions. Assume that in-city mileage for this model is approximately normally distributed with standard deviation of 1.5 miles per gallon. What is the probability that a person who will purchase this model, will end up with a car that averages between 26 and 30 miles per gallon for in-city driving? a. 5 points) (5 points) b. Find the value of the 90th percentile, Pso, for this random variable. Use information from part (b) to circle the correct choice and to fill in the blanks in the following sentence c. (2 points) % of the new model cars average (at least/at most) miles per gallon for in-city driving. Show your work. Partial credit will be given.
math   Statistics-And-Probability   
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1) Given example Mean H 28 Standard deviation σ 1.5 Now calculate P(cars average between 26 and 30 miles per gallion) iep( 26 < x< 30)-P(0 < z <-)+p(0 < z< ) 30-28 26-28 1.5 800 -P (0 z<1.33)P(0 <-1.33) P (26 < x< 30) = 0.4082 + 0.4082 P(26 < x < 30) = 0.8164 P(26 < x < 30 )-81.64% 2) 90thpercentile 28 + 1.282*1.5 The exact z value holding 90% of the value 1.282 which is determined from table of standard normal probabilities with more precision. P9o 29.92 81.64 % of the new model cars average (at least /at most) 29.92 miles per gallon for in-city driving. 3)

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