A computer laboratory in a school has 33 computers. Each of the 33 computers has 90% reliability. Allowing for 10% of the computers to be down, an instructor specifies an enrollment ceiling of 30 for his class. Assume that a class of 30 students is taken into the lab.
a. What is the probability that each of the 30 students will get a computer in working condition?
b. The instructor is surprised to see the low value of the answer to (a) and decides to improve it to at least 95% by doing one of the following:
i. Decreasing the enrollment ceiling.
ii. Increasing the number of computers in the lab.
iii. Increasing the reliability of all the computers.
To help the instructor, find out what the increase or decrease should be for each of the three alternatives.