Question: A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of $2\mathrm{.}0$ per minute. In serving themselves, customers take about $26$ seconds, exponentially distributed. a$.$ How many customers would you expect to see on the average at the coffee urn? $($Do not round intermediate

A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of $2\mathrm{.}0$ per minute. In serving themselves, customers take about $26$ seconds, exponentially distributed.

a$.$ How many customers would you expect to see on the average at the coffee urn? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Average no of customers $=?$

b$.$ How long would you expect it to take to get a cup of coffee? $($Round your answer to $2$ decimal places.$)$

Expected time $=?$ Minutes

c$.$ What percentage of time is the urn being used? $($Do not round intermediate calculations. Round your answer to $1$ decimal place.$)$

Percentage of time $=?\%$

d$.$ What is the probability that three or more people are at the coffee urn? $($Do not round intermediate calculations. Round your answer to $1$ decimal place.$)$

Probability $=?\%$

e$.$ If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of $26$ seconds, how many customers would you expect to see at the coffee urn $($waiting and$/$or pouring coffee$)?($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Average no of customers $=?$

f$.$ If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of $26$ seconds, how long would you expect it to take $($in minutes$)$ to get a cup of coffee, including waiting time? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Expected time $=?$ minutes

Please show excel sheet or other working document if possible, thank you.