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 6.208

26. Due-Date Babies. Only 4% of babies are born on their due dates.9 Massachusetts General Hospital in Boston assists in the delivery of 142 babies per 2-week period.10 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 babies will be born on their due dates during a two-week period.
  4. Approximate the probability that at least one baby will be born on its due date during a two-week period.