question 2 5 126 wi fi interruptions refer to example 5 27 page 262 in

Question

Question 2: 5.126 [
Wi-Fi interruptions. Refer to Example 5.27 (page 262), in which we were told that the mean number of Wi-Fi interruptions per day is 0.9. We also found in Example 5.27 that the probability of no interruptions on a given day is 0.4066.
a. Treating each day as a trial in a binomial setting, use the binomial formula to com- pute the probability of no interruptions in a week.
b. 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?
c. Based on the Poisson mean of part (b), use the Poisson distribution to compute the probability of no interruptions in a week. Confirm that this probability is the same as that found part (a). Explain in words why the two ways of computing no interruptions in a week give the same result.
d. 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 the probability that only one interruption occurs during the week