A doctorhas developed an experimental drug for toe-nail fungus. He needs to test it out on some people to make sure it works. He has a list of 2000 people who could be potential subjects in his study. 1120 of these potential subjects have toe nail fungus. A random sample of 75 people will be drawn from this pool and surveyed about whether they have toe-nail fungus. Let F be the number of people in the sample with toe-nail fungus.
a) Define F 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 toe-nail fungus?
c) Set up an equation to find the probability that exactly 40 people in his sample had toe-nail fungus. Fill in all the values, but do not solve.
d) What is a good approximation for the random variable described in this scenario and what are its parameters? Why are you able to use this approximation?
e) What is the approximate probability that 40 people in his sample have toe-nail fungus