Question: A company with equipment on multiple lines used to manufacture its products schedules each line for maintenance on a weekly basis. This scheduled maintenance is a complete check of the line that includes any needed adjustments to the equipment. When this scheduled is followed there is a 0.02 probability that line’s equipment will need additional minor maintenance the day of the scheduled service, a 0.10 probability it will need minor maintenance the first day following the service, a 0.27 probability it will need minor maintenance the second day following service, a 0.43 it will need minor maintenance the third day and a 0.18 probability it will need minor maintenance the fourth day following the scheduled service. (This covers the 5 regular working days for the plant. Hint: Let 0 represent the day of the scheduled service.)

a. Set up a probability distribution to describe this situation. (2 points)

b. Based on this schedule for full maintenance of the lines, how often should they expect to need to complete minor maintenance? (This would be the mean of the distribution.) Be sure to explain what this number represents. (5 points)

c. How much would this value reasonably be expected to fluctuate? (This is the standard deviation.) Be sure to explain what this number represents. (5 points)

d. What’s the probability of needing to do maintenance within the first three days following the scheduled service? (3 points)