George Pourbabaee Owns a Gas Station Using the Following Random Number Sequence: 92, 44, 15, 97

question 45

Essay

George Pourbabaee owns a gas station. The cars arrive at the gas station according to the following inter-arrival time distribution. The time to service a car is given by the following service time distribution.
$$\begin{array} { | c | c | c | c | c | c | }\hline \begin{array} { c } \text { Interarrival } \\\text { time (in } \\\text { minutes) }\end{array} & \mathbf { P ( X ) } & \begin{array} { c } \text { Random } \\\text { Numbers }\end{array} & \begin{array} { c } \text { Service Time } \\\text { (in minutes) }\end{array} & P ( \mathbf { X } ) & \begin{array} { c } \text { Random } \\\text { Numbers }\end{array} \\\hline 4 & .35 & 00 - 34 & 2 & .30 & 00 - 29 \\\hline 7 & .25 & 35 - 59 & 4 & .40 & 30 - 69 \\\hline 10 & .30 & 60 - 89 & 6 & .20 & 70 - 89 \\\hline 20 & .10 & 90 - 99 & 8 & .10 & 90 - 99 \\\hline\end{array}$$
Using the following random number sequence: 92, 44, 15, 97, 21, 80, 38, 64, 74, 08, estimate the average customer waiting time, average idle time of the assistant, and the average time a car spends in the system.

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Definitions:

Scarce Resources

Resources that are limited in availability and are not enough to fulfill the wants and needs of the population.

Group Boundaries

Defined or perceived limits that specify who belongs to a particular social group or category, distinguishing members from non-members.

Asch Experiment

A social psychology experiment by Solomon Asch studying if and how individuals yielded to or defied a majority group and the effect of such influences on beliefs and opinions.

Group Conformity

The phenomenon where individuals adjust their behaviors, attitudes, or beliefs to match those of the group to which they belong, often due to real or perceived pressure.