Suppose the average waiting time for a customer\'s call to be answered by a comp

Question

Suppose the average waiting time for a customer's call to be answered by a company representative is five minutes. (a) Find the probability that a call is answered during the first minute. (b) Find the probability that a customer waits more than five minutes to be answered. (a) We are given that the mean of the exponential distribution is mu = 5 min and so, from the result of Example 3, we know that the probability density function is f(t) = {0 if t 5) = integral^infinity_5 f(t) dt = integral^infinity_5 0.2e^-t/5 dt = lim_x rightarrow infinity integral^x_5 0.2e^-t/5 dt = lim_x rightarrow infinity (e^-1 - e^-x/5) = 1/e almostequalto 0.368 About 37% of customers wait more than five minutes before their calls are answered. Find the median waiting time for a phone call to the company described in this example. () ______ min

Explanation / Answer

here as we get from above that CDF=P(T<t)=1-e-t/5

hence median will occur at t for P(T<t)=0.5=1-e-t/5

e-t/5 =0.5

taking log on both sides and solving

t=-5*log(0.5) =3.47 minutes

please revert

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