Problem: You have joined a large auto parts manufacturer as a first line supervisor. The assembly line has 18 positions that must be filled with your 20 employees. Two of the twenty serve as "utility operators" and fill in for bathroom breaks and supply parts to the assembly line. Well, things go well when all 20 are at work; however, this only happens about 95% of the time. Considering sickness, vacation and other reasons employees are not at work consumes about 13 days a year. If all 20 are at work, you can produce 1100 alternators per day. If the number falls to 19 your production will be 1000. For 18 employees, 900 alternators will be produced. For 17 employees in attendance 400 will be produced. Although awkward with 16 you can produce 200 alternators. Now if less than 16, show up for work, the line is stopped and your employees are temperately assigned to work on other products in the factory. Use the binomial distribution and assume the probability of an employee being at work is 95 percent.
a) For any random selected day, what is the probability that all 20 employees will be in attendance?