Question

A store averages 8 customers per hour.

The statement above appears like this problem will be dealing with the poisson distribution. however, the questions that follow refer to the amount of time between customers making them an exponential problem.

what is the probability the store goes more than 3 minutes between customers?
P(X > 3) =

Answer 1

The probability of the store going more than 3 minutes between customers can be found using the exponential distribution. The average time between customers is 7.5 minutes and the probability is approximately 0.6706.

Step-by-step explanation:

The probability of the store going more than 3 minutes between customers can be found using the exponential distribution.

Since the average number of customers per hour is 8, we can find the average time between customers by dividing 60 minutes by 8. This gives us an average of 7.5 minutes between customers.

To find the probability that the store goes more than 3 minutes between customers, we can use the cumulative distribution function for the exponential distribution.

The cumulative distribution function is given by P(X < x) = 1 - e^(-λx), where λ is the rate parameter.

In this case, λ = 1/7.5 = 0.1333.

Plugging in x = 3, we get

P(X > 3) = 1 - P(X < 3)

1 - (1 - e^(-0.1333 * 3)) = e^(-0.3999)

P(X > 3) ≈ 0.6706.