High School

A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 19.8 pounds and a standard deviation of 3.2 pounds.

If a sampling distribution is created using samples of the amounts of weight lost by 99 people on this diet, what would be the mean of the sampling distribution of sample means?

Answer :

The mean of the sampling distribution of sample means for samples of size 99 is 19.8 pounds.

To find the mean of the sampling distribution of sample means, we need to understand a few key points about the Central Limit Theorem (CLT).

According to the CLT, the mean of the sampling distribution of sample means (also known as the expected value) is equal to the mean of the population distribution from which the samples are drawn. This remains true regardless of the sample size.

  1. Identify the mean of the population distribution.
  2. Recognize that the mean of the sampling distribution of sample means is equal to the population mean.

Using these steps, we determine that the mean of the sampling distribution of sample means is:

[tex]\mu_{\bar{x}} = \mu =[/tex] 19.8 pounds

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