# Statistics

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The inside diameter of the automobile wheel bearing sets at a factory is expected to be normally distributed with a mean of 1.30inches and a standard deviation of 0.04 inches.

What is the probability that a randomly selected wheel bearing will have an inside diameter of,
a) between 1.28 and 1.30 inches?
b) between 1.31 and 1.33 inches?
c) between what two values (in terms of inside diameter) will 60% of the wheel bearings fall?

If 16 random samples of 16 wheel bearings were selected,
d) what proportion of the sample means would be between 1.31 and 1.33 inches?
e) compare your results in B and D

• Statistics -

(A-C) Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores. Reverse the process with the 60% (.60).

(D) Here you are dealing with a distribution of means rather than raw scores.

Z = (score-mean)/SEm

SEm = SD/√n

Use same table.

• Statistics -

.967

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