Consider the following hypothesis test.

H₀: 10

H_a: < 10

The sample size is 155 and the population standard deviation is assumed known with = 5. Use = 0.05.

(a) If the population mean is 9, what is the probability that the sample mean leads to the conclusion do not reject H₀?

(Round your answer to four decimal places.)

(b) What type of error would be made if the actual population mean is 9 and we conclude that H₀: 10 is true?

(c) What is the probability of making a type II error if the actual population mean is 8? (Round your answer to four decimal places. If it is not possible to commit a type II error enter NOT POSSIBLE.)