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 55% of the respondents do believe inequality is too large.

1. 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.
   
   f (2) =
   
2. In a sample of six British citizens, what is the probability that at least two respondents believe that inequality is too large? If required, round your interim calculations and final answer to four decimal places.
   
   P (at least 2) =
   
3. In a sample of four British citizens, what is the probability that none believe inequality is too large? If required, round your answer to four decimal places.
   
   f (0) =

Answer 1

Since the survey found that the 55 % of the respondents do believe inequality is too large, hence p=0.55 now using binomial distribution

a) P(X=k)

The formula used is

at k=2 and n=6

P(X=2) =0.1861

b) Now P(X=at least 2 )=P(X>=2)

=1-P(X<2)

=1-{P(X=0)+P(X=1}

=0.9308

c) again, P(X=0)

at n=4

using above formula

=0.0410

The probabilities are calculated directly using the formula in software.