People goto Sams Shop randomly and independently of each other at a rate of 15 per day,on (average). It's open from 7am - 5pm and a customer arrives. What's the standard deviation between customers?

Answer 1

There is a relationship between the Poisson and the negative exponential distribution: the negative exponential distribution for time until next arrival equals the Poisson for total counts with the same rate. Then, the expected time until next arrival for the negative exponential = 1/rate

The rate is 15/ day= 15/time between 7 am and 5 pm = 15/10 hours = 3/2 hours

Then, the expected time until next arrival is 1/(3/2 hours) = 2/3 hour = 40 minutes.