MATH SOLVE

9 months ago

Q:
# Solve by poisson distribution: A store has an average of 90 customers per hour. a) What is prob. that for 2 minutes the store does not receive any customers? b) Among 100 identical stores, how many would not receive any customers?

Accepted Solution

A:

a) What is the probability that for 2 minutes the store does not receive any customers?
First, we need to find the average rate of customer arrivals for 2 minutes. There are 60 minutes in an hour, so for 2 minutes, the rate can be calculated as follows:
Rate for 2 minutes = (2/60) * 90 customers = 3 customers
Now, we can use the Poisson distribution formula to calculate the probability of receiving 0 customers in 2 minutes:
P(X = 0) = (e^(-Ξ») * Ξ»^0) / 0!
Where:
Ξ» (lambda) is the average rate of customer arrivals for 2 minutes, which is 3 in this case.
e is the base of the natural logarithm (approximately 2.71828).
P(X = 0) = (e^(-3) * 3^0) / 0!
P(X = 0) = (e^(-3) * 1) / 1
P(X = 0) = e^(-3)
Using a calculator:
P(X = 0) β 0.0498 (rounded to four decimal places)
So, the probability that the store does not receive any customers in 2 minutes is approximately 0.0498 or 4.98%.