Question: You have an \[\bar{x}\] chart monitoring your production process. You are using a Shewhart Control chart with 2.75??limits which means that the probability of getting an out of control signal when the process is in control is p = .006.

a. What is the probability of getting a false alarm on the very next sample?

b. What is the probability of not having a false alarm in the next 10 samples?

c. If we sample every 45 minutes, how long (in hours) will we go on average between false alarms?

d. If the mean shifts to ? + 1??(an out of control state), what is the probability of getting a false alarm on the very next sample?