A manufacturer of ice pops fills each plastic container with a fruity liquid, leaving enough room so that consumers can freeze the product. A filling machine is set so that the amount of liquid in...

A manufacturer of ice pops fills each plastic container with a fruity liquid, leaving enough room so that consumers can freeze the product. A filling machine is set so that the amount of liquid in each ice pop is normally distributed with mean 8.00 ounces and standard deviation 0.25 ounce. Suppose 16 ice pops are randomly selected.

a. Find the probability distribution of the sample mean number of ounces in each container, X .

b. Find the probability that the sample mean is less than 7.9 ounces.

c. Find the probability that the sample mean is more than 8.15 ounces.

 d. Suppose the filling machine operator can fine-tune the process by controlling the standard deviation of the fill. Find a value for s such that the probability that the sample mean is more than 8.05 ounces is 0.05.