A hospital has three emergency generators for use in case of a power failure. Each generator operates independently and the manufacturer claims that the probability each generator will function properly during a power failure is 0.95. Let X be the number of emergency generators that will fail during the next power outage.

a. What code can you use to compute the probability that two of the backup generators will fail, P(X=2)?

b. What quantity does the expression 1-P(X=3) represent ?

c. Consider a sample of 1000 generators from this population of generators that are claimed to fail only 5% of the time. Let X be the number of generators that fail in the sample of 1000. Though X is a Binomial RV, it can be roughly approximated by a Normal random variable with mean and standard deviation given in the discussion handout.

What code can be used to approximate the probability that 55 or fewer of the 1000 generators experience a failure using a normal approximation?