An automobile manufacturer produces a certain model of car. The fuel economy fig

Question

An automobile manufacturer produces a certain model of car. The fuel economy figures of these cars are normally distributed with a mean mileage per gallon (mpg) of 36.8 and a standard deviation of 1.3. (a) What is the probability that one of these cars will have an mpg of more than 37.5? (b) What is the probability that one of these cars will have an mpg of less than 35? l (c) What is the probability that one of these cars will have an mpg of less than 40? (d) What is the probability that one of these cars will have an mpg of between 34 and 38 mpg? (e) What is the minimum mpg of the 15% most fuel efficient cars? (f) What is the maximum mpg of the 10% least fuel efficient cars

Explanation / Answer

Mean. =36.8

Standard deviation = 1.3

A. Z = (37.5-36.8)/1.3 = 0.5384

From z table,

P(Xbar>37.5) = 1-P(Xbar<37.5) = 1-0.7054 = 0.2946

B. Z = (35-36.8)/1.3 = -1.3846

From z table

P = 0.0838 or 8.38%

C. Z = (40-36.8)/1.3 = 2.4615

P = 0.9931

D. P(34<xbar<38) = P(xbar<38)-P(Xbar<34)

Z = (38-36.8)/1.3 = 0.9230

Z = (34-36.8)/1.3 = -2.1538

P(34<xbar<38) = 0.821

2- 0.0158 = 0.8054

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