A certain genetic mutation occurs in a population with probability 0.05. A researcher has geneticmaterial from 40 unrelated members of this population and tests for the mutation.

(a) Suppose the researcher finds that 3 people in a given sample of 40 unrelated members of thispopulation have the genetic mutation. Give the summary table and bar graph for this outcome.

(b) Explain why the number of people in this sample of 40 unrelated members of this population withthis genetic mutation has a binomial distribution.

(c) Use R to calculate the probability that at least 1 person in a sample of 40 unrelated members ofthis population will have the genetic mutation.

(d) Use R to calculate the probability that no more than 3 people in a sample of 40 unrelated membersof this population will have the genetic mutation.

(e) What is the mean number of people with the genetic mutation in a sample of 40 unrelated membersof this population?

(f) What is the variance and standard deviation of the number of people with the genetic mutationin a sample of 40 unrelated members of this population?

(g) Use R to produce a graph of the distribution of the number of people with the genetic mutationin a sample of 40 unrelated members of this population. Describe the shape of the distrib