Question

In a survey of US adults with a sample size of 2005, 390 said Franklin Roosevelt was the best president since World War II. TWO US adults are selected at random from this sample without replacement Complete parts (a) through (d). through (d). (a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II The probability that both adults say Franklin Roosevelt was the best president since World War II is (Round to three decimal places as needed.) (b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II. The probability that neither adult says Franklin Roosevelt was the best president since World War Ilis (Round to three decimal places as needed.) (e) Find the probability that at least one of the two adults says Franklin Roosevelt was the best president since World War il Ibra ents The probability that at least one of the two adults says Franklin Roosevelt was the best president since World War ilis (Round to three decimal places as needed) (d) Which of the events can be considered unusual? Explain. Select all that apply.

Answer 1

Here is same for all, n=2 is constant, events are independent and only two outcomes

390 P = 2006 = 0.195

Hence properties of binomial distribution are satisfied

So we will use binomial distribution to find required probabilities by using excel formula of binomial distribution

a.

P(=2) = BINOMDIST(2,2,0.195,0) = 0.038

b.

P(x=0) = BINOMDIST(0,2,0.195,0) = 0.648

c.

Plx>1)= 1-P.1 <1) = 1-P(x = 0) = 1-BINOMDIST(0,2,0.195,0) = 1 - 0.6480 = 0.352

d. As probability of P(x=2)=0.038 is less than 0.05, hence it is unusual.