Please help with questions e and f. All other questions are correct. Grades for

Question

Please help with questions e and f. All other questions are correct.

Grades for Shelbi Gillen/X y D ch 7 practice Problem C| ezto.mheducation.com/hm.tpx Chegg Study | Guided S × . A Cafetena Serving Line shelbi × Close | A cafeteria serving line has a coftee urn from which customers serve themselves. Arrivals at the urn follow a Polsson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed. a. How many customers would you expect to see on the average at the coffee urn? Average no of customers b. How long would you expect it to take to get a cup of coffee? Expected time 1 minute(s) C. What percentage of time is the urn being used? 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.) 75 % Probability 42.15% e. if the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 15 seconds, how many customers would you expect to see at the cotfee um (waiting and/or pouring coffee)? (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 15 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time? (Round your answer to 2 decimal places.) 7-23 PM 11/11/2017

Explanation / Answer

Arrival rate (A) = 3 per min

Service rate (S) = 15 seconds or 4 per min

e) Average number of customers for constant service time (Lq) = A^2/(2*S*(S-A)) = 3^2/(2*4*(4-3)) = 9/8 = 1.13

f) Total time = Lq/A+1/S = 1.13/3 + 1/4 = 0.63 min

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