Question

Problem 3-11 (Algorithmic) A recent survey by the New Statesman on British social attitudes asked respondents if they believe that inequality is too large. The survey found that 70% of the respondents do believe inequality is too large. In a sample of six British citizens, what is the probability that two believe inequality is too large? If required, round your answer to four decimal places.

Answer 1

Answer: 0.0595

Explanation:

The formula for binomial distribution :-

`P(x)= ^nC_xp^x(1-p)^(n-x)`, where P(x) is the probability of success in x trials ,n is the sample size and p is the population proportion for each trial.

Given : Proportion of respondents do believe inequality is too large : p= 0.7

Sample size :n=6

Then , the probability that two believe inequality is too large:-

`P(2)= ^6C_2(0.7)^2(0.3)^(4)\\\\=(6!)/(2!(6-2)!)(0.7)^2(0.3)^(4)\\\\=0.059535\approx0.0595`

Hence, the probability that two believe inequality is too large = 0.0595