Assume that the price of regular unleaded gasoline across th

Assume that the price of regular unleaded gasoline across the nation is normally distributed with a mean of 2.44 and standard deviation of .28.

If all possible samples of size 50 from the population of these gasoline prices are drawn and the mean is found for each sample, describe the shape and scaling (mean/st.dev) on the graph of the sampling distribution for these sample mean values as theorized by the Central Limit Theorem.

Solution

The central limit theorem says that:

1. The sampling distirbution of the means will be approximately normal.

2. It will have a mean that is the same as the population mean, so u(X) = 2.44.

3. It will have a standard deviation that is given by sigma/sqrt(n) = 0.28/sqrt(50) = 0.03959798.