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The weights of adult individuals in a certain country are normally distributed with a population mean of [tex]\mu = 172[/tex] pounds and a population standard deviation of [tex]\sigma = 29[/tex] pounds. Suppose [tex]n = 36[/tex] individuals are sampled.

1. What is the mean of the sampling distribution of the means?

Answer :

The sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.


In the context of sampling distribution of the means, the standard deviation represents the degree of spread or variation of sample means around the true population mean.

To compute the standard deviation of the sampling distribution of the means, one typically divides the population standard deviation by the square root of the sample size.

Therefore, the standard deviation of the sampling distribution of the means is 29/√36 = 29/6 = 4.83 pounds.

So, the sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.

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