When interpreting control charts, one of the three out-of-control criteria is that there are eight consecutive points all above or all below the centerline. For a statistically stable process, there is a 0.5 probability that a point will be above the centerline and a 0.5 probability that a point will be below the centerline. In each of the following, assume that sample values are independent and the process is statistically stable.
a. Find the probability that when eight consecutive points are randomly selected, they are all above the centerline.
b. Find the probability that when eight consecutive points are randomly selected, they are all below the centerline.
c. Find the probability that when eight consecutive points are randomly selected, they are all above or all below the centerline.