5.69 Cyberbullying. An online survey, in partnership with Habbo, was conducted to study cyberbullying among 13- to 25-year-olds in the United Kingdom. It was reported that 62% of the young people had received nasty private messages on a smartphone social network app.19 You randomly sample four young people from the United Kingdom and ask them if they’ve received nasty messages. Let X be the number who say Yes.

  1. (a) What are n and p in the binomial distribution of X?

  2. (b) Find the probability of each possible value of X, and draw a probability histogram for this distribution.

  3. (c) Find the mean number of positive responders and mark the location of this value on your histogram.