Anne runs a small shop where she provides a service. She is able to process

an average of $9$ customers per hour. An average of $4$ customers per hour seek

this service at her shop. What is:

$5.$ the probability that Anne will not be working with a customer

$($no customers$)$ when the shop phone rings?

$6.$ the probability of $3$ customers in the system?

$7.$ the average time a customer spends waiting in line $($in minutes$)?$

$8.$ the average number of customers waiting in line?

$9.$ the average number of customers in the system?

Anne would like to be serving customers $70\%$ of the time.

$10.$ What must the arrival rate be for Anne to stay that busy?

Do not round to an integer.

$**$Be sure to use at least four significant digits past the decimal. Recall that

we start counting after the zero values $($e$.$g$.,0\mathrm{.}001234$ is $4$ significant digits$).$