A distribution of service times at a waiting line indicates that service takes 12 minutes 30% of the time and 14 minutes 70% of the time. Prepare the probability distribution, the cumulative probability distribution, and the random number intervals for this problem. The first six random numbers were 99, 29, 27, 75, 89, and 78. What is the average service time for this simulation run?

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Katie Coffey · Accepted Answer

Final Answer :   Service   time   Probability   Cumulative   probability   Random   number   intervals   Simulation   frequency  12 . 30 . 30 01 − 30 2 ( 29 , 27 ) 14 . 70 1.00 31 − 00 4 ( 99 , 75 , 89 , 78 ) \begin{array} { | c | c | c | c | c | } \hline \begin{array} { c } 	ext { Service } \	ext { time }\end{array}  &  	ext { Probability }  &  \begin{array} { c } 	ext { Cumulative } \	ext { probability }\end{array}  &  \begin{array} { c } 	ext { Random } \	ext { number } \	ext { intervals }\end{array}  &  \begin{array} { c } 	ext { Simulation } \	ext { frequency }\end{array} \\hline 12  &  .30  &  .30  &  01 - 30  &  2 ( 29,27 ) \\hline 14  &  .70  &  1.00  &  31 - 00  &  4 ( 99,75,89,78 ) \\hline\end{array}  Service   time  ​ 12 14 ​  Probability  .30 .70 ​  Cumulative   probability  ​ .30 1.00 ​  Random   number   intervals  ​ 01 − 30 31 − 00 ​  Simulation   frequency  ​ 2 ( 29 , 27 ) 4 ( 99 , 75 , 89 , 78 ) ​ ​   The average service time is 2 ∗ 12 + 4 ∗ 14 = 80 / 6 = 13.33 minutes.

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