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:

Sample Mean

The average value of a sample set of numbers, calculated by adding all the values together and dividing by the number of values.

Sampling Distribution

The probability distribution of a statistic based on a large number of samples or replicates.

Probability Distribution

Describes how the probabilities are distributed over the values of a random variable.

Expected Value

The expected value of a variable, determined by summing up all possible values, each weighed by its probability of happening.