Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 6.5 per year. a. Find the probability that, in a year, there will be 4 hurricanes. b. In a 35-year period, how many years are expected to have 4 hurricanes? c. How does the result from part (b) compare to a recent period of 35 years in which 3 years had 4 hurricanes? Does the Poisson distribution work well here? a. The probability is (Round to three decimal places as needed.) b. The expected number of years with 4 hurricanes is (Round to one decimal place as needed.) close to / very different from c. The result from part (b) is the number of hurricanes in the recent period of 35 years, so the Poisson distribution appear to work well in the given situation. does / does notThe random variable x represents the number of phone calls an author receives in a day, and it has a Poisson distribution with a mean of 8.6 calls. What are the possible values of x? Is a value of x = 3.3 possible? Is x a discrete random variable or a continuous random variable? What are the possible values of x? O A. 0, 1, 2, 3, .. OB. 1, 2, 3, . . O C. any real number greater than or equal to 0 and less than or equal to 8.6 O D. any real number greater than or equal to 0 Is a value of x = 3.3 possible? Is x a discrete random variable or a continuous random variable? A value of x = 3.3 possible because x is a random variable. is / is not discrete / continuousIn a recent year, an author wrote 183 checks. Use the Poisson distribution to find the probability that, on a randomly selected day, he wrote at least one check. The probability is (Round to three decimal places as needed.)