Question

During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes. a. What is the expected number of calls in one hour? per hour b. What is the probability of three calls in five minutes (to 4 decimals)? c. What is the probability of no calls in a five-minute period (to 4 decimals)?

Answer 1

a) Let X be the number of calls in 60 minutes The rate of 1 calls in 2 minutes is same as 1/2 60 30 in 60 minutes X follows Poisson distribution with parameter (rate) A 30 X ~ Poisson (λ= 30) Mean of poisson random variable is equal to its rate parameter λ Mean or expected value, E(X)-μ- 30.0000 b) Let X be the number of calls in 5 minutes The rate of 1 calls in 2 minutes is same as 1/2 5 2.5 in 5 minutes X follows Poisson distribution with param eter (rate) λ-2.5 XPoisson (A 2.5) e-XX* e2.5(2.5)3 (0.082085) x (15.625) P(X = 3) =-k! Use excel function POISSON.DIST( X, mean, cumulative) to calculate Px(3): POISSON.DISTL 3, 2.5, FALSE ) 0.213 763 01725 3! P(X 3)- 0.2138 P(X 0), λ = 2.5 e-2.5(25)0-(0.082085)×(1) -0.082 085 k! 0! Use excel function POISSON.DIST( X, mean, cumulative) to calculate Px(0): POISSON.DIST( 0, 25, FALSE ) 0.082084 9986239 P(X 0)0.082.1 @seoThank ,youJ0户