The heat evolved in calories per gram of a cement mixture is approximately normally distributed with a standard deviation of 2. We wish to test 0H: = 100 versus 1H: 100 with a sample of size 5. If the rejection region is defined as x < 98.5 and x> 101.5, then find:

a. , the type I error probability; b. , the type II error probability, for the case when the true mean heat evolved is 103; and c. the power of the test when the true mean heat evolved is 103.