5.102 Wi-fi interruptions. Suppose that the number of wi-fi interruptions on your home network follows the Poisson distribution with an average of 0.9 wi-fi interruptions per day.
(a) Show that the probability of no interruptions on a given day is 0.4066.
(b) Treating each day as a trial in a binomial setting, use the binomial formula to compute the probability of no interruptions in a week.
(c) Now, instead of using the binomial model, let’s use the Poisson distribution exclusively. What is the mean number of wi-fi interruptions during a week?
(d) Based on the Poisson mean of part (c), use the Poisson distribution to compute the probability of no interruptions in a week. Confirm that this probability is the same as found part (b). Explain in words why the two ways of computing no interruptions in a week give the same result.
(e) Explain why using the binomial distribution to compute the probability that only one day in the week will not be interruption free would not give the same probability had we used the Poisson distribution to compute that only one interruption occurs during the week.