Question 662268: Most four-year automobile leases allow up to 77,000 miles. If the lessee goes beyond this amount, a penalty of 20 cents per mile is added to the lease cost. Suppose the distribution of miles driven on four-year leases follow the normal distribution. The mean is 65,000 miles and the standard deviation is 5,000 miles.
a. What percent of the leases will yield a penalty because of excess mileage?
b. A low mileage car is defined as one driven in the lowest 5% of a car mileage. How many miles, at most, must a car be driven to be defined as a low mileage car?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Most four-year automobile leases allow up to 77,000 miles. If the lessee goes beyond this amount, a penalty of 20 cents per mile is added to the lease cost. Suppose the distribution of miles driven on four-year leases follow the normal distribution. The mean is 65,000 miles and the standard deviation is 5,000 miles.
a. What percent of the leases will yield a penalty because of excess mileage?
z(77000) = (77000-65000)/5000 = 12/5 = 2.4
P(x > 77000) = P(z > 2.4) = normalcdf(2.4,100) = 0.0082
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b. A low mileage car is defined as one driven in the lowest 5% of a car mileage. How many miles, at most, must a car be driven to be defined as a low mileage car?
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invNorm(0.05) = -1.645
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Find x using x = z*s+u
milage = -1.645*5000+65000 = 56,776 miles
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Cheers,
Stan H.
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