Consider the following hypothesis test.

H₀: u ≥ 10

H_a: u < 10

The sample size is 120 and the population standard deviation is assumed known with s = 5. Use a = .05.

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

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

c. What is the probability of making a type ii error if the actual population mean is 8?