Is the following situation a binomial setting? Explain how it does or does not meet the conditions of a binomial setting.

A manufacturer produces a large number of microwaves. From past experience, the manufacturer knows that approximately 1.5% of all their microwaves are defective. Consumer Reports randomly selects 20 of these microwaves for testing. We want to determine the probability that no more than one of these microwaves is defective?

In the workplace, racial discrimination is a very serious issue. Consider a company in which 20% of the employees are African-American. At the end of the year, promotions are awarded to a group of employees. Out of the 40 promotions awarded, five are African-American. Given that the awarding follows the binomial distribution, B(40,.2). a) How many African-Americans would you expect to get promotions? b) What is the probability that five African-Americans receive promotions? c) What is the probability that five or fewer African-Americans receive promotions? d) Do you think the company is suspect of racial discrimination? Explain your thinking.

a) What is the probability that exactly one of the microwaves is defective?

b) What is the probability that at most two of the microwaves are defective?

c) Find the mean and standard deviation.