J-Mart is a small convenience store close to the KU campus. The store has a single checkout counter staffed by one employee at all times. Customers arrive at the checkout counter following a Poisson process with an average rate of 6 customers/hr. The time taken by the employee to complete the checkout process is also random with a mean of 3 minutes a standard deviation of 1.5 minutes.

1.) How long (in minutes) does the entire checkout process (waiting in line and then checking out) take for an average customer?If your answer is not an integer, provide at least three decimal places, e.g., 7.500.

2.) On average, how many customers are present in the checkout area (i.e., either checking out or waiting in line)? If your answer is not an integer, provide at least three decimal places, e.g., 7.500.

3.) What is the probability that the checkout process (waiting in line and then checking out) for a customer takes more than 5 minutes? Please enter your answer as a value between 0 and 1. If your answer is not an integer, provide at least three decimal places, e.g., 7.500.

4.) What is the probability that there is one or more customers waiting in line for the checkout process? Please enter your answer as a value between 0 and 1. If your answer is not an integer, provide at least three decimal places, e.g., 7.500.

Hint: You need to carefully think about how many customers should be in the checkout area before a line starts forming!