Dr. Fred Reesurch has developed an experimental drug for treating eczema (a skin disease). He needs to test it out on some people to make sure it works. He has a list of 5000 people who could be potential subjects in his study. 1550 of the potential subjects have eczema. A random sample of 75 people will be drawn from this pool and surveyed about their disease history. Let X be the number of people in the sample with eczema.

a) Define X in terms of the story and name the distribution and its parameters.

b) What is the expected number of people in his sample that have eczema?

c) Set up an equation to find the probability that exactly 20 people in his sample had eczema.

d) What is a good approximation for this story and what are its parameters?

e) What is the approximate probability exactly 20 people in his sample have eczema?