The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with sigma = 0.30 and that mean = 5.25.

(b) If the true average percentage is mu = 5.6 and a level alpha = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from the null hypothesis? (Round your answer to four decimal places.)

(c) What value of n is required to satisfy alpha = 0.01 and Beta(5.6) = 0.01? (Round your answer up to the next whole number.)