Answer to Question #266700 in Statistics and Probability for Faith

Question

On average, 6 customers make purchases every 2 hours at a certain hardware. Assume that the number of customers making purchases follows a Poisson distribution. If a customer has just made a purchase, calculate (to 4 decimal places) the probability that the time until the next customer arrives to make a purchase is less than 5 minutes

Answer 1

Let X be a random variable represents the number of customers making purchase in 5 minutes.

Then X ~ $Pois(\lambda)$ , where $\lambda=5*{\frac 6 {120}}=0.25$

We have to find P(X > 0) = 1 - P(X = 0)

$P(X = x) = {\frac {\lambda^x} {x!}}e^{-\lambda}$

$P(X>0) = 1-P(X = 0) = 1-{\frac 1 1}e^{-0.25}=1-0.7788=0.2212$