A bottling machine can be regulated so that it discharges the average of (u) ounces per bottle. It has been observed that amount of fill dispensed through the machine is usually distributed with sd(o) = 1ounce. A sample of n=9 filled bottle is randomly selected.
a) Find out the probability that the sample mean will be within .3 ounce of true mean (u) for that specific setting.
b) How many observations should be included in the sample if we wish that sample mean to be within .3 ounces of u with probability .95?