A Design Engineer Wants to Construct a Sample Mean Chart

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, on what sample(s) (if any) does service life appear to be out of control?

A) sample 1
B) sample 2
C) sample 3
D) both samples 2 and 3
E) all samples are in control

Correct Answer:

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