Question

93. At a 911 call center, calls come in at an average rate of one call every two minutes. Assume that the time that elapses from one call to the next has the exponential distribution. Where appropriate, round answers to three decimal places (i.e. 0.123)

a. On average, how much time occurs between five consecutive calls? Answer

minutes

b. Find the probability that after a call is received, it takes more than three minutes for the next call to occur. Answer

c. Ninety-percent of all calls occur within how many minutes of the previous call? Answer

d. Suppose that two minutes have elapsed since the last call. Find the probability that the next call will occur within the next minute. Answer

Answer 1

a)expected time =5*2 =10 minutes

b)for exponential distribution : parameter =2

P(X>3) =1-P(X<3 )=1-(1-e^-3/2) =0.223

c)

pth percentile =-β*ln(1-p)

therfore 90th percentile =

-2*ln(1-90/100)=

4.605 minutes

d)

P(X<1) =1-e^-1/2 =0.393