The Quality of a Device Should Be Examined in the Inspection

question 5

Essay

The quality of a device should be examined in the inspection department sequentially in three steps before it is sent to packaging department. The probability distributions for the time required to complete each of the activities are as follows:
​ $$\begin{array} { | c | c | c | } \hline \text { Step } & \begin{array} { c } \text { Time } \\\text { (minutes) }\end{array} & \text { Probability } \\\hline 1 & 3 & 0.15 \\\hline & 5 & 0.25 \\\hline & 7 & 0.35 \\\hline & 9 & 0.25 \\\hline 2 & 11 & 0.25 \\\hline & 13 & 0.30 \\\hline & 15 & 0.45 \\\hline 3 & 8 & 0.35 \\\hline & 10 & 0.20 \\\hline & 12 & 0.45 \\\hline\end{array}$$ ​
a. Construct a spreadsheet simulation model to estimate the average time spent in inspection department and the standard deviation of the time spent in inspection department.
b. What is the estimated probability that the inspection will be completed in 32 minutes or less?

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Definitions:

Subconscious Awareness

The part of the mind that is not currently in focal awareness yet influences thoughts, feelings, and actions.

Higher-Level Consciousness

This is a state of awareness that involves focused attention and control over mental processes.

Lower-Level Consciousness

A state of minimal awareness and attention, such as that experienced during drowsiness or light sleep.

Automatic Processes

Cognitive activities that occur with little to no conscious effort or control, such as breathing or driving a familiar route.