Compute the population mean using the normal distribution.

The actual amount of instant coffee that a filling machine puts into 4-ounce jars may be looked upon as a random variable having a normal distribution with σ =0.04 ounce.

a). If only 2 percent of the jars are to contain less than 4 ounces, what is the mean fill of these jars?

b). If the variability of the filling machine is reduced to 0.025 ounce, verify that this will lower the required average amount of coffee to 4.050 ounces and yet keep 98 percent of the jars above 4 ounces.