Question

In a sample of 2091 U.S.​ adults, 388 said Franklin Roosevelt was the best president since World War II. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​ adults, complete parts​ (a) through​ (d)

(a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II. (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. (ROUND TO THREE DECIMAL PLACES AS NEEDED)

(c) Find the probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II. (ROUND TO THREE DECIMAL PLACES AS NEEDED)

(d) Which of the events can be considered​ unusual? Explain. Select all that apply

1.The event in part​ (b) is unusual because its probability is less than or equal to 0.05.

2.None of these events are unusualNone of these events are unusual

3.The event in part (a) is unusual because its probability is less than or equal to 0.05

4.The event in part​ (c) is unusual because its probability is less than or equal to 0.05

Answer 1

a)

Two U.S. adults are selected at random from the population of all U.S. adults without replacement Let us assume there is an event with each of two adults where = i th adult dine out at a restaurant more than once per week.

Now assuming the sample is representative of all U.S. adults,, here we have,

(a) The probability that both adults dine out more than once per week.

= 388/2091*387/2090

=0.03435914685

b)

the probability that neither adult says Franklin Roosevelt was the best president since World War II

= (2091 - 388)/2091 * (2090- 388)/2090

= 0.663244

c)

P(X >= 1)

= 1 - P(X = 0)

= 1 - 0.663244

= 0.33675515252

d)

3.The event in part (a) is unusual because its probability is less than or equal to 0.05