Problem 7.43 A chemical plant superintendent orders a process readjustment (namely shutdown and setting change) whenever the pH of the final product falls below 6.92 or above 7.08. The sample pH is normally distributed with unknown mu and standard deviation 0.08.

Determine the probability: (a) of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is operating as intended and mu=7.0 probability=?

(b) of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is slightly off target, namely the mean pH is mu=7.02, which is slightly too high but still in the prescribed interval.

probability=?

(c) of failing to readjust (that is, the probability that the measurement is in the acceptable interval) when the process mean pH is mu=7.11, which is too alkaline.

probability=?

(d) of failing to readjust (that is, the probability that the measurement is in the acceptable interval) when the process mean pH is mu=6.86, which is too acidic.

probability=?