A baby food company is trying to set control limits on its machine that fills jars of strained apple sauce. The weight of the contents of each jar should be greater than 135g and less than 139g at the same time. The known standard deviation of the net weight is = 0.6g.

a) What probability distribution or density function would you assume for the weights? Why?

b) Determine the range of acceptable value for the mean which will achieve both of the following objectives:

Probability that a jar is underfilled <= 0.001 Probability that a jar is overfilled <= 0.005