Aboveground swimming pools are very popular in some parts of the country. The vinyl liners used in these pools vary in thickness, but most pools are sold with a 15- or 16-mil-thick liner.31 A certain...

Aboveground swimming pools are very popular in some parts of the country. The vinyl liners used in these pools vary in thickness, but most pools are sold with a 15- or 16-mil-thick liner.31 A certain company sells special liners and claims the mean thickness is 20 mil. Suppose the thickness of these liners is normally distributed with standard deviation 0.63. A random sample of these vinyl liners was obtained and the thickness of each was carefully measured. The resulting data are given in the following table.

a. Suppose the company’s claim is true. Find the distribution of the mean thickness of these liners.

b. Use the data to determine whether there is any evidence to suggest that the company’s claim is false.