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# Unusal Observation

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The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean be considered unusual.
For a sample of n=65, find the probability of a sample mean being greater than 228 if &#956; =227 and &#963; = 3.9 .
For a sample of n=65, find the probability of a sample mean being greater than 228 if &#956; =227 and &#963; = 3.9 is ____. Round to four decimal places as needed.

Would the given sample mean be considered unusual?
The sample mean would or would not be considered be considered unusual because it lies or does not lie within 1 standard deviation, 2 standard deviations, or 3 standard deviations of the mean of the sample means.

© BrainMass Inc. brainmass.com September 19, 2018, 11:27 pm ad1c9bdddf - https://brainmass.com/math/probability/unusual-observation-statistics-297080

#### Solution Preview

If Xbar is the sample mean, then we have,
Z = (Xbar - &#956;)/(&#963;/&#8730;n) = ((Xbar-227)/(3.9/&#8730;65) follows a Standard Normal distribution.

P[Xbar > 228] = P[(Xbar-227)/(3.9/&#8730;65) > ...

#### Solution Summary

The solution contains the determination of the unusual sample mean for a given probability distribution.

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