Poisson Distribution?

Question

The number of passengers arriving at a check out counter of an airport follows Poisson distribution. On the average 6 customers arrive every 5-minutes. The probability that over any 10-minute interval, exactly 8 passengers will arrive at the check out counter is what number?  

 

 

Answer 1

Formula: p(x) = (λ^xe^-λ)/x!

 

λ  is your long-run average. You need your units to match and cannot change x, so 6 customers/ 5 minutes = 12 customers/ 10 minutes. 12/10 = 1.2

 

x = the number you are trying to find the probability of, in this case 8.

 

e = 2.71828... (it's an irrational number, just like Pi).

 

p(8) = (1.2⁸×e^-1.2)/8!

 

 

I will leave the calculation to you. If you would like more Stat help via online tutoring, let me know.