A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons. The survey found that 23% of the respondents have boycotted goods for ethical reasons. Answer the following questions using the binomial probability distribution.
a. In a sample of six British citizens, what is the probability that two respondents have boycotted goods for ethical reasons? (Show all calculations to earn credit.)
b. In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons? (Show all calculations to earn credit.)
c. In a sample of six British citizens, what is the probability that at most two respondents have boycotted goods for ethical reasons? (Show all calculations to earn credit.)
d. In a sample of ten British citizens, what is the probability that none of the respondents have boycotted goods for ethical reasons? (Show all calculations to earn credit.)