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
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"
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