## Question 619:

1

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One of the main tenets of the central limit theorem is that the distribution of the sample means will be approximately normally distributed regardless of what the parent population shape or distribution are. In other words, if we take repeated samples from this population and we plotted each of the means from the samples, this distribution will be normal, especially as our sample gets above 30. So we'd therefore expect the shape of this sampling distribution to be symmetric and normal.

What is the mean value for this sampling distribution? =  The mean for the sample of means would equal the mean of the population mean, assuming the sample is large enough. So we'd expect the mean to be 20.84 lbs.

What is the standard deviation of this sampling distribution?

The standard deviation of the sample means, or of any sample, is also called the standard error of the mean, or SEM. The SEM is the standard deviation divided by the square root of the sample size = s/SQRT(n).  So we don't know what the sample standard deviation of the sample means would be since that is not provided. This relationship shows that as the sample gets larger the "error" or variability around the sample mean will decrease.

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