A process is monitored by taking samples at regular intervals and is declared to be out of control if a point plots outside the 3σ control limits on an  chart. Assume the process is in control.
a. What is the probability that a false alarm will occur within the next 50 samples?
b. What is the probability that a false alarm will occur within the next 100 samples?
c. What is the probability that there will be no false alarm within the next 200 samples?
d. Fill in the blank: The probability is 0.5 that there will be a false alarm within the next samples.