1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability Density

  1. Nov 12, 2012 #1
    The manager of a fast food restaurant determines that the average time that her customers wait for their food is 2.5 minutes. The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. She doesn't want to give away free hamburgers to more than 2% of her customers. What should the advertisement say?

    I'm solving for [itex]t[/itex]:

    [itex]\int_ 0.4e^{-t/2.5}~dt=0.02[/itex]

    [itex]-e^{-t/2.5}=0.02[/itex]

    [itex]0=0.02+e^{-t/2.5}[/itex]

    Take the natural logs and add [itex]-t/2.5[/itex] to get it back on the other side.

    [itex]t/2.5=-3.91[/itex]

    [itex]t=-1.56[/itex]

    The answer is ten minutes. What did I do wrong?
     
    Last edited: Nov 12, 2012
  2. jcsd
  3. Nov 12, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You cannot have exp(-t/2.5) = -0.02, since the exponential function is always > 0. You did the integration incorrectly.

    RGV
     
  4. Nov 12, 2012 #3

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You need to show the limits of the integral and calculate with them. The probability that somebody is not served for x minutes is

    [tex]\int _x^\infty{0.4 e^{-0.4 t}dt}=0.02[/tex]

    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Probability Density
  1. Probability - density (Replies: 12)

  2. Probability density (Replies: 10)

  3. Probability Density (Replies: 6)

  4. Probability Density (Replies: 11)

Loading...