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# (Solved): In The EAI Sampling Problem, The Population Mean Is $51,100 And The Population Standard Deviation Is...

In the EAI sampling problem, the population mean is $51,100 and
the population standard deviation is $4,000. When the sample size
is *n* = 20, there is a 0.4977 probability of obtaining a
sample mean within +/- $600 of the population mean. Use
*z*-table.

- What is the probability that the sample mean is within $600 of
the population mean if a sample of size 40 is used (to 4
decimals)?

- What is the probability that the sample mean is within $600 of the population mean if a sample of size 80 is used (to 4 decimals)?

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### Expert Answer

Solution: We are given: a. We have to find: Using the z-score formula, we have: