Question

the time between calls to a plumbing supply business is exponentially distributed withh a mean time bwtween calls of 10 minutes

mean time between calls of 10 minutes 1 (a) What is the probability that there are no calls within a 10-miwate Interval? (b) What is the probability that at least one call serivos within a 1s misvute interval? (e) Determine the lengsh of an interval of time such thai the probability of no ealls in the Interval is 0.40.

Answer 1

here for exponential distribution parameter $\beta$ =10

a)P(no call in 10 minutes) =P(X>10)=e^{-x/ $\beta$} =e^-10/10 =0.3679

b)P(X<15)=1-e^-15/10 =0.7769

c) length of interval =- ^{$\beta$ *ln(p) =}-10*ln(0.4)=9.1629 miunute