Benzene is a chemical used in dry cleaning. A manufacturer claims the mean ppm(parts per million) meets the federal standard that it be below 7970 ppm (parts per million) of benzene. To test this hypothesis, 16 samples of the exit water were taken and found that have a sample average of 7965 ppm. Historical data show that the population variance is 203 ppm^2. A hypothesis test is done to determine if the federal standard is being met.

a) What is the numerical value of the population standard deviation?

b) What is the probability of type II error if the true population mean is 7960 and Type I error probability is 0.05?