**Please help solve this problem. Thanks **

The mean of the distribution of maximum car mileage is 150,000 miles with a standard deviation of 20,000 miles. Assume that the distribution approximates a Bell curve.

a. Use the z-table calculator and find the maximum mileage for a car which is the 85th percentile. Use value from an area. (Show a screen shot for your answer.)

http://davidmlane.com/hyperstat/z_table.html

b. What is the z-score for this mileage? z-score = (x-µ)/σ

c. Suppose you pick a single car at random. What is the probability that the maximum mileage will be between 170,000 and 200,000 miles? Use area from a value. (Show a screen shot for your answer.)

Use the central limit theorem to the following questions.

d. Suppose you pick a group of 25 cars instead. What would be the standard deviation of the sample's (group's) average? (i.e. σ_{xbar} = σ/)

e. What is the probability that a group of 25 cars will have an average maximum mileage between 170,000 and 200,000 miles? Use the z-table calculator with "area from a value". (Show a screen shot for your answer.)

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