The distribution of pH levels for all community swimming pools in a large county is approximately Normal with mean 7.5 and standard deviation 0.2. According to swimming pool studies, the safest pH levels for water in swimming pools are between 7.2 and 7.8. Consider the situation in which the health inspector find 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.