The duration of time it takes General Motors to build a car is normally distributed with a mean of 31 hours and a standard deviation of 2 hours.

Question

a) What is the probability that a single car, selected at random,
will take between 28 and 34 hours?
b) What is the probability that the mean of the times for a sample
of 25 cars will be between 28 and 34 hours?

Answer 1

a) Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.

b) Z = (score-mean)/SEm

SEm = SD/√n

Use the table.

Answer 2

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