Question

(3 points) The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.71. Please give your answers to two decimal places. Parta) What is the probability that the time between consecutive customers is less than 15 seconds? Part b) Find the probability that the time between consecutive customers is between ten and fifteen seconds. Part ) Given that the time between consecutive customers arriving is greater than ten seconds, what is the chance that it is greater than fifteen seconds?

Answer 1

solution: Gillen Data Mean +0.71 X = Goxo. H = 42.6 aj we have to find probabinty that less than 15 seconds. We use exponential distribution . formula - f(x) = fxetx , X30 0,aco PLX415) = 1 -exp/ - 1-0.7032009 = 0.2968 0:30) o we have to find probability that between 10 and 15 seconds. p(102x<15) = P(x+10) - P(x<15) =1-e* l-e-! 151x helola 2049078-0-40320 - 10.09 to probability greater greater 10 seconds (() we have than and seconds 15 P(x3151x310) = p(x=15 nx>10) PLY P(x>10) 0.40320 0.74078 = 10.89