Question

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. You randomly samplefour 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.

   My editions:

4. d) Based on your answer to part b, what is the probability that you select at least 3 young people who say Yes? Is it appropriate to use the normal distribution to find this probability?

5. e) Suppose that you are instead sampling from 200 students. Now, X is Binomially distributed with n=200 and p=0.62. You want to find the probability that at least 140 young people say Yes. Is it appropriate to use the Normal Approximation? Why or why not?

6. f) Find the probability that at least 140 young people say Yes in a sample of 200.

7. g) Rework your answer to part f, using the continuity correction.

Answer 1