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# Question about Compute the probability

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A population of unknown shape has a mean of 75. You select a sample of 40. The standard deviation of the sample is 5. Compute the probability the sample mean is:
a. Less than 74.
b. Between 74 and 76.
c. Between 76 and 77.
d. Greater than 77.

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#### Solution Preview

Assuming that Central Limit Theorem holds,and use the z distribution tables for calculations:

For this problem the STD of the sample mean is 5/sqrt(40) = 0.7906 .
So we have a normal distributed ramdom variable X with mean Mu = 75
and standard deviation StD = 0.7906

-Compute the probability the sample ...

#### Solution Summary

This solution explains how the central limit theorem is used to estimate the mean of a sample based on information about the population.

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