Q$4.$ Amazon AWS has a customer service center at Dearborn handling calls from customers encountering system issues. The center operates $24$ hours a day, seven days a week. Managers at the center also expect the number of customer calls to follow a Poisson distribution and have an average of $576$ calls per day.

Calculate the average number of calls in a one$-$hour interval, a $30-$minutes interval, and a $5$minutes interval.

What is the probability of having ten calls during a $30-$minutes interval? Express the PMF formula and parameter values clearly and respond at the $4^{th}$ decimal place.

What is the probability of no calls during a $5-$minutes interval? Express the PMF formula and parameter values clearly and respond at the $4^{th}$ decimal place.

What is the probability of more than two calls in a $5-$minutes interval Express the PMF formula and parameter values clearly and respond at the $4^{th}$ decimal place.

How to obtain the probability that less than two calls during a $5-$minutes interval using Excel? express the Excel formula clearly