can anyone answer this statistics multiple choice question about probability?

Question

Question:

As the saying goes, "You can't please everyone." Studies have shown that in a large population approximately 4-5% of the population will be displeased, regardless of the situation. If a random sample of 25 people are selected from such a population, what is the probability that at least two will be displeased? 

Answers:

A) 0.045

B) 0.311

C) 0.373

D) 0.627

E) 0.688

Answer 1

Can use binomial distribution to compute this probability. Use 0.045 as the probability of being displeased (halfway between 4 and 5 percent). Probability at least two will displeased is 1 - probability(0 or 1 will be displeased) = 1 - probability 0 will be displeased - probability 1 will be displeased.

0 25

probability 0 will be displeased = C 0.045 0.955 = 0.316

25 0

1 24

probability 1 will be displeased = C 0.045 0.955= 0.373

25 1

so probability at least two will be displeased is 1 - 0.316 - 0.373 = 0.311 (B)