Chemists use pH to measure the acid/alkaline nature of compounds. A large vat of mixed commercial chemicals is supposed to have a mean pH of 6.3 and a standard deviation of 1.9 . Assume a normal distribution for pH values. If a random sample of 10 readings in a vat is taken and the mean pH is computed, find each of the following:
a) P(5.2 <= xbar)
b) P(xbar<=7.1)
c) P(5.2<= xbar<=7.1)