A recent survey by the New Statesman on British social attitudes asked responden

Question

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 59% of the respondents do belie e inequality is too large. a. 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)- b. In a sample of slx British citizens, what is the probablity that at least two respondents belleve that Inequality Is too large? If required, round your Interlm calculations and final answer to four declmal places P (at least 2)- In a sample of four British citizens, what is the probability that none believe inequality is too large?Irequired, round your answer to four decimal places (O

Explanation / Answer

Here ............... we take P = 0.59 and Q = 0.41

Using the binomal probability function ............ f(x) = ncx (p)x * (q)n-x  

Question -a

f(2) = 6C2 (0.59)2 * (0.41)6-2 = 15 * 0.3481 * 0.02825761 = 0.1475

Question - b

At least 2 = 1 - f(0) - f(1) = 1 - [ 6C0 (0.59)0 * (0.41)6-0 ] - [ 6C1 (0.59)1 * (0.41)6-1 ]   

= 1 - [ 1 * 1 * 0.004750104241 ] - [ 6 * 0.59 * 0.0115856201 ]

= 1 - 0.00475 - 0.0410 = 0.9543

Question - c

f(0) = 6C0 (0.59)0 * (0.41)6-0 = 1 * 1 * 0.004750104241 = 0.0048

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