The Numbers of Defective Items Produced by a Machine Over

question 58

Essay

The numbers of defective items produced by a machine over the last 25 days are as follows:

$$\begin{array} { | c | l | l | l | l | l | l | l | l | } \hline 19 & 6 & 15 & 20 & 17 & 16 & 17 & 12 & 15 \\\hline 29 & 23 & 17 & 7 & 10 & 14 & 14 & 27 & 22 \\\hline 8 & 5 & 23 & 19 & 9 & 28 & 5 & & \\\hline\end{array}$$ a. Construct a frequency distribution and a relative frequency distribution for these data. Use five class intervals, with the lower boundary of the first class being five items.
b. Construct a relative frequency histogram for these data.
c. What is the relationship between the total area under the histogram you have constructed and the relative frequencies of observations?

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Definitions:

Marginal Utility

An additional amount of satisfaction gained from consuming an extra unit of a good, highlighting the concept of diminishing returns.

Total Utility

The total satisfaction received from consuming a certain amount of goods or services.

Corn Dogs

A popular snack consisting of a hot dog coated in a thick layer of cornmeal batter and deep-fried.

Marginal Utility

The additonal satisfaction or utility that a person receives from consuming an additional unit of a good or service.