Please do not answer the question if you can\'t answer it step by step with comp
ID: 3154440 • Letter: P
Question
Please do not answer the question if you can't answer it step by step with complete formula to be able to understand.
A grocery store has only one checkout counter. Customers arrive at this checkout at
random from 1 to 8 minutes apart each possible value of inter-arrival time has the same
probability of occurrence as given below. Analyze the system by simulating the arrival
of 20 customers using the random numbers 913, 727, 15, 948, 309, 922, 753, 235, 302,
109, 93, 607, 738, 359, 888, 106, 212, 493 and 535. Also, calculate the average time
between arrival
Distribution of time between arrivals
Time Arrivals Probability
(Minutes)
1 0.125
2 0.125
3 0.125
4 0.125
5 0.125
6 0.125
7 0.125
8 0.125
Explanation / Answer
The distribution of time between arrivals is
Given 20 customers using the random numbers 913, 727, 15, 948, 309, 922, 753, 235, 302, 109, 93, 607, 738, 359, 888, 106, 212, 493 and 535
The time-between-arrival determination is shown in above table. Observe that the first random digits are 913. To obtain the corresponding time between arrivals, enter the fourth column of above table and read 8 minutes from the first column of the table.Alternatively, we see that 0.913 is between the cumulative probabilities 0.876 and 1.000, again resulting in 8 minutes as the generated time
Time between arrivals Probability Cumulative Probability Random - Digit Assignment 1 0.125 0.125 000-125 2 0.125 0.250 126-250 3 0.125 0.375 251-375 4 0.125 0.500 376-500 5 0.125 0.625 501-625 6 0.125 0.750 625-750 7 0.125 0.875 751-875 8 0.125 1.000 876-1000