Assume that the requirements for the Poisson probability distribution are met for Exercises 23–31. Also, when asked to approximate a probability, use the Poisson approximation for the binomial distribution.

Question 6.213

31. Teens in Virtual Worlds. According to a Pew Research study, 10% of teenagers participate in online virtual worlds such as Second Life, Gaia, or Habbo Hotel.13 Suppose that we take a sample of 100 teenagers. Do the following:

  1. Verify that the requirements are met for using the Poisson distribution to approximate the binomial distribution.
  2. Find the mean of the Poisson distribution used to approximate the binomial distribution.
  3. Approximate the probability that teenagers participate in such online virtual worlds.
  4. Approximate the probability that either 10, or 11, or 12 teenagers participate in such online virtual worlds.

6.3.31

(a) and (b) 10 (c) 0.1251 (d) 0.3336