Question

A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January 28, 2008). The survey found that 23% of the respondents have boycotted goods for ethical reasons.

a) In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?

b) In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?

c) In a sample of ten British citizens, what is the probability that between 3 and 6 have boycotted goods for ethical reasons? d) In a sample of ten British citizens, what is the expected number of people that have boycotted goods for ethical reasons? Also find the standard deviation.

Answer 1

X ~ B ( n = 6 , P = 0.23 )

Part a)

Part b)

P(X = 0 ) = 0.2084
P(X = 1 ) = 0.3735

P ( X >= 2 ) = 1 - P ( X <= 1 ) = 1 - 0.5819 = 0.4181

Part c)

P(X = 3 ) = 0.2343
P(X = 4 ) = 0.1225
P(X = 5 ) = 0.0439
P(X = 6 ) = 0.0109
P ( 3 <= X <= 6 ) = 0.4116

Part d)

Mean = n * P = ( 10 * 0.23 ) = 2.3
Variance = n * P * Q = ( 10 * 0.23 * 0.77 ) = 1.771
Standard deviation = (variance) = (1.771) = 1.3308