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:

Black Magic

Practices of magic that are intended to invoke supernatural powers for malevolent purposes.

Susto

A cultural illness primarily found in Latin America, described as a condition of intense fear believed to stem from a traumatic event causing the soul to leave the body.

Taijin-kyofusho

A Japanese culture-specific syndrome characterized by an intense fear that one's body, body parts, or bodily functions are displeasing or offensive to others.

Amok

A culturally bound syndrome primarily observed in Southeast Asia, characterized by a sudden outburst of violent behavior, often driven by a perceived slight or insult.