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 August 3rd, 2017, 01:37 PM #1 Member   Joined: Apr 2017 From: PA Posts: 45 Thanks: 0 Let $X$ be the total service time for $10$ customers. Estimate the probability that Assume that the service time for a customer at a bank is exponntially distributed with mean service time $2$ minutes. Let $X$ be the total service time for $10$ customers. Estimate the probability that $X > 22$ minutes. Attempt: I tried to set up and take the integral $$\int_{22}^{+infinity} λe^{10x}\,\mathrm dx$$ then I eventually did the integral and did an inegtration by parts many times. unfortunately I was unable to figure this out August 3rd, 2017, 04:54 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,529 Thanks: 1389 1 customer has average service time 2 min implies 10 customers have average serving time 20 minutes. Note that the serving time is the inverse of the rate. The distribution of $X$ is thus $f_X(t) = \dfrac {1}{20} e^{-\frac {t}{20}}$ \begin{align*} &P[X > 22] \\ \\ &= \displaystyle \int_{22}^{\infty}~f_X(t)~dt \\ \\ &= 1 - \int_{0}^{22}~f_X(t)~dt \\ \\ &= 1 - \int_{0}^{22}~\dfrac {1}{20} e^{-\frac {t}{20}} ~dt \\ \\ &= e^{-\frac{22}{20}} \\ \\ &\approx 0.333 \end{align*} Tags $10$, $x$, customers, estimate, probability, service, time, total Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post marks2014 Probability and Statistics 3 April 30th, 2014 12:23 PM sthoriginal Advanced Statistics 0 February 25th, 2014 07:52 AM Pherion Probability and Statistics 1 June 13th, 2013 12:01 AM rnck Probability and Statistics 7 November 5th, 2011 08:33 PM

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