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. Construct a probability distribution for the problem and use both the probability mass function and the cumulative probability function to answer the questions where appropriate.

In a sample of ten British citizens, what is the probability that between 3 and 6 have boycotted goods for ethical reasons?