In a sample of 2061 U.S adults, 365 said Franklin Roosevelt was the best preside

Question

In a sample of 2061 U.S adults, 365 said Franklin Roosevelt was the best president since World War I. 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 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 l (Round to three decimal places as needed) (c) Find the probability that at least one of the two adults says Fr as needed) (d) Which of the events can be considered unusual? Explain Select ll that apply of the two adults says Franklin Roosevelt was the best president since World Wrl(Round to three decimalplaces None of these events are unusual

Explanation / Answer

Solution:

We have to use hyper-geometric distribution for finding

P(X=x) = SCs*(N – S)C(N – s) / NCn

Where,

S = successes from population

s = successes from sample

N = Population size

n = Sample size

We are given

N = Population size = 2061

S = successes from population = 365

n = Sample size = 2

Part a

We have to find P(X=2)

We have N = 2061, S = 365, n = 2, s = 2

P(X=2) = 2C2*(2061 – 365)C(2061 – 2)/2061C2 = 0.031293

Required probability = 0.031

Part b

We have to find P(X=0)

We have N = 2061, S = 365, n = 2, s = 0

P(X=0) = 2C0*(2061 – 365)C(2061 – 0)/2061C2 = 0.677096

Required probability = 0.677

Part c

We have to find P(X1)

P(X1) = 1 – P(X=0)

P(X1) = 1 – 0.677

P(X1) = 0.323

Required probability = 0.323

Part d

Event in part a is unusual because probability is less than 0.05.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.