The county health inspector will select a random sample of 4 community swimming pools in the county to investigate the pH levels. (b) Describe the sampling distribution of the sample mean for samples of size 4.

(c) Consider the situation in which the health inspector finds the sample mean of the 4 pools to be outside the safe pH levels. As a result, the inspector declares that the population mean is not 7.5. However, if the population mean really is 7.5, the inspector will have made an error. Such an error is called a Type I error. Find the probability that the inspector will make a Type I error with the sample of 4 pools. Show your work.

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