Find the median waiting time for a phone call to the company described in this e

Question

Find the median waiting time for a phone call to the company described in this example. () _____ min Suppose the average waiting time for a customer's call to he answered by a company representative is five minutes. Find the probability that a call is answered during the first minute. Find the probability that a customer waits more than five minutes to he answered. SOLUTION 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^-t/5) = 1/e = 0.368 About 37% of customers wait more than five minutes before their calls are answered.

Explanation / Answer

for medain waithing time CDF P(X<x) =0.5

hence 1-e-x/5 =0.5

e-x/5 = 0.5

taking ln and solving

x/5 =ln(2)

x=3.46574

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