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If it is assumed that the heights of men are normally distributed with a standard deviation of 2.5 inches, how large a sample should be taken to be fairly sure (probability 0.95) that the sample mean does not differ from the true mean (population mean) by more than 0.90 in absolute value? (Round your answer up to the nearest whole number.)

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Answer:

30 men

Step-by-step explanation:

In order to be sure that the sample mean does differ from the population mean by more than 0.90, the sample size (n) that should be used is given by:

[tex]0.90 < Z\frac{s}{\sqrt{n}}[/tex]

Where 'Z' , for a 95% probability is 1.960, 's' is the standard deviation of 2.5 inches:

[tex]0.90 > 1.960\frac{2.5}{\sqrt{n}}\\n >(\frac{1.960*2.5}{0.9})^2\\n>29.64[/tex]

Rounding up to the nearest whole number, the sample size should be at least 30 men.

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