Suppose small aircraft arrive at a certain airport

Problem 85E Answer: Step1: We have Suppose small aircraft arrive at a certain airport according to a Poisson process with rate =8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter = 8t. We need to find, a. What is the probability that exactly 6 small aircraft arrive during a 1-hour period At least 6 At least 10 b. What are the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period c. What is the probability that at least 20 small aircraft arrive during a 2.5-hour period That at most 10 arrive during this period Step2: Let “X” the number of small aircraft that arrive during time t and it follows poisson distribution parameter “” The probability mass function of poisson distribution is given by e x P(X) = x! , x = 0,1,2,3,...,n. Where, (mean of the poisson distribution) a). Given that time period t = 1hr. Then, = 8t = 8(1) = 8 Now, The probability that exactly 6 small aircraft arrive during a 1-hour period is given by P(exactly 6 small aircraft arrive during a 1-hour period) = P(X = 6) Consider, e (8)6 P(X = 6) = 6! 0.000335(262144) = 720 = 87.8182 720 = 0.1219. Therefore,The probability that exactly 6 small aircraft arrive during a 1-hour period is 0.1219. 1).P( t least = P(X 6)