The Quality of a Device Should Be Examined in the Inspection

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?