Question

The number of requests to a towing company is a Poisson distribution with μ=20 per day. The company provides service 7 days a week.

a. Calculate the probability of receiving 10 requests in a typical day.
b. Find the expected number of requests in a week.

Answer 1

The probability of receiving 10 requests in a typical day is 0.0608. The expected number of requests in a week is 140.

Step-by-step explanation:

To calculate the probability of receiving 10 requests in a typical day, we can use the Poisson distribution formula:

P(x; μ) = (e^(-μ) * μ^x) / x!

where x is the number of requests, μ is the average number of requests per day, and e is the base of the natural logarithm.

In this case, μ = 20, and x = 10. Plugging these values into the formula, we get:

P(10; 20) = (e^(-20) * 20^10) / 10!

Simplifying further, the probability is approximately 0.0608.

To find the expected number of requests in a week, we can multiply the average number of requests per day by the number of days in a week:

Expected number of requests in a week = μ * number of days in a week = 20 * 7 = 140.