Assume that the fill, X, of a water filling machine is 12.2 with a standard deviation of 0.1 with the measurements being in liquid ounces. Assume X is a normal random variable. Suppose we...

Assume that the fill, X, of a water filling machine is 12.2 with a standard deviation of 0.1 with the measurements being in liquid ounces. Assume X is a normal random variable. Suppose we independently take 50 such measurements, say X1, X2, ….., X50. Let M be the sample mean of the 50 measurements. Let S be the sum of the 50 measurements.

h) What is the standard deviation of M-12.2?


i) What is the probability that M-12.2>.01?


j) What is the standard deviation of 50*(M-12.2)?