A Design Engineer Wants to Construct a Sample Mean Chart

question 48

Multiple Choice

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: $$\begin{array} { c c c c c } \text { Sample } &&{ \text { Service Life (hours) } } \\\hline 1 & 495 & 500 & 505 & 500 \\2 & 525 & 515 & 505 & 515 \\3 & 470 & 480 & 460 & 470\end{array}$$
If he uses upper and lower control limits of 520 and 480 hours, what is his risk (alpha) of concluding that service life is out of control when it is actually under control (Type I error) ?

• A) 0.0026
• B) 0.0456
• C) 0.3174
• D) 0.6826
• E) 0.9544

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Definitions:

Phosphate

A salt or ester of phosphoric acid, commonly used in fertilizers, detergents, food additives, and for water treatment.

Degradable Wastes

Wastes that can break down into less harmful components over time through biological processes.

Dissolved Oxygen

The amount of oxygen gas dissolved in water, essential for the respiration of aquatic life.

Sewage Treatment

A process of removing contaminants from wastewater, primarily from household sewage, to produce an effluent that is suitable for discharge or reuse.