Question
A water treatment plant needs to maintain the pH of the water in the reservoir at a certain level. To monitor this, they take 2 oz. of water at 37 locations every hour, measure the pH at each of those locations, and find their average.
Normal Distribution
When the sample size is at least 30 and the sample is selected with replacement then the sampling distribution of the sample means can be considered approximately normal. The mean of the sample means is equal to the population mean.
Question
A water treatment plant needs to maintain the pH of the water in the reservoir at a certain level. To monitor this, they take 2 oz. of water at 37 locations every hour, measure the pH at each of those locations, and find their average.
Normal Distribution
We can find probabilities using the normal distribution when we know that the specified data are normally distributed. We also use the central limit theorem in the sampling distribution of means when the sample size is greater than 30.