A factory employs several thousand workers, of whom 20% are Hispanic. If the 17 members of the union executive committee were chosen from the workers at random, the number of Hispanics on the committee would have the binomial distribution with n = 17 and p = 0.20.
(a) What is the mean number of Hispanics on randomly chosen committees of 17 workers?
(b) What is the standard deviation sigma of the count X of Hispanic members?
(c) Suppose that 10% of the factory workers were Hispanic. Then p = 0.1.
What is sigma in this case? what is sigma if p = 0.01?
What does your work shown about the behavior of the standard deviation of a binomial distribution as the probability of a success gets closer to 0?
A. As p increases, σ
increases.
B. As p increases, σ
decreases.
C. As p decreases, σ
increases.
D. As p decreases, σ
decreases.