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 6.212

30. Social Media-Driven Holiday Sales. IBM reported that 1% of Black Friday purchases on ecommerce Web sites were driven directly by social media. Suppose that we take a sample of 200 such purchases. 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 purchase was driven by social media.
  4. Approximate the probability that at least one purchase was driven by social media.