Lilly's Bakery has a single cashier. Customers arrive at a rate of 3 per hour. Customers are served at an average rate of 4 per hour. Assume that arrivals are random, and service times are exponentially distributed.

a) What is the probability that exactly 5 people arrive during a given one hour period?

b) What is the probability that Lilly is idle (i.e., not serving any customers)?

c) What is the average time a customer spends in the bakery before receiving her order?

d) If Lilly believes the average time in (c) is too long, briefly describe her options for improving the system.

e) What is the probability that there are 4 people in the store (not including Lilly)?

f) What is the probability that the time it takes Ellie to serve a customer is exactly 2 minutes?

g) If the average arrival rate increases to 5 per hour, find the average number of people on line.

Lilly's cousin Edie wants a job. Edie can also serve customers exponentially at an average rate of 4 per hour. Customers continue to arrive randomly at an average rate of 3 per hour. With both working:

h) What is the probability that either Lilly or Edie (but not both) is idle?

i) What is the probability that there are 4 customers in the store (not counting Lilly and Edie)?

Lilly's Bakery has a single cashier. Customers arrive at a rate of 3 per hour. Customers are served at an average rate of 4 per hour. Assume that arrivals are random, and service times are exponentially distributed.

a) What is the probability that exactly 5 people arrive during a given one hour period?

b) What is the probability that Lilly is idle (i.e., not serving any customers)?

c) What is the average time a customer spends in the bakery before receiving her order?

d) If Lilly believes the average time in (c) is too long, briefly describe her options for improving the system.

e) What is the probability that there are 4 people in the store (not including Lilly)?

f) What is the probability that the time it takes Ellie to serve a customer is exactly 2 minutes?

g) If the average arrival rate increases to 5 per hour, find the average number of people on line.

Lilly's cousin Edie wants a job. Edie can also serve customers exponentially at an average rate of 4 per hour. Customers continue to arrive randomly at an average rate of 3 per hour. With both working:

h) What is the probability that either Lilly or Edie (but not both) is idle?

i) What is the probability that there are 4 customers in the store (not counting Lilly and Edie)?