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.
- Identify the mean of the population distribution.
- 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