Question

1. A factory employs several thousand workers, of whom 30% are Hispanic. If the 15 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 = 15 and p = 0.3.

1. Verify the situation is indeed a Binomial experiment. You could assume that there are more than 1,500 workers employed in the factory (Hint: check the four conditions) [2]
2. What is the probability that exactly 3 members of the committee are Hispanic? [1]
3. What is the probability that 3 or fewer members of the committee are Hispanic? [1]
4. What is the mean number of Hispanics on randomly chosen committees of 15 workers in Exercise 5.58? [1]
5. What is the standard deviation σ of the count X of Hispanic members? [1]

f. Suppose that 10% of the factory workers were Hispanic. Then p = 0.1. What is σ in this case? What is σ if p = 0.01? What does your work show about the behavior of the standard deviation of a binomial distribution as the probability of a success gets closer to 0?

Answer 1

n--х 15 3 3 12- c) 13 012969

3.15 11u8 4) 15% D. Į > 0,9 1.35 : σ = 1.1619 JL5 X О.ol у О.cn 0.1485 σ : 0.385 As