The number of customers entering a 24-hour convenience store every 10-minutes can be modeled by the Poisson distribution with a mean of λ=4 customers. You are to look at the amount of time passing between successive customers entering the convenience store, represented by X.

Q1: How many minutes can you expect to pass between successive customers entering the convenience store? I got 4/10 = 2.50 which is correct.

Q2: What is the probability at most 2.5 minutes will pass between the arrival of one customer and the next customer? In answering this question, be sure to use your answer in (a) to two decimals. Enter your answer using four decimals, and, if necessary, use your answer in part (a).

What I think should be done.. P(X≤2.5)= 0.2381 as calculated in my minitab software. However this is incorrect apparently.. :(

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What am I doing wrong?

  • 4
    $\begingroup$ The waiting time between Poisson events has an exponential distribution $\endgroup$ – David Quinn Mar 9 '18 at 20:55
  • $\begingroup$ Oh yeah that would explain it. $\endgroup$ – Amanda O Mar 9 '18 at 21:01
  • $\begingroup$ For more on connections btw Pois and Exponential see this Q&A. $\endgroup$ – BruceET Mar 9 '18 at 23:21

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