A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test H₀: μ = 175 millimeters versus H₁: μ > 175 millimeters, using the results of n = 10 samples. 

(a) Find the type I error probability α if the critical region is x̅ > 185.

(b) What is the probability of type II error if the true mean foam height is 185 millimeters?

(c) Find β for the true mean of 195 millimeters.