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A Design Engineer Wants to Construct a Sample Mean Chart

question 59

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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:  Sample  Service Life (hours)  149550050550025255155055153470480460470\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?

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Definitions:

Beginning Balance

The amount of money or value available in an account at the start of a new financial period.

Ending Balance

The amount of money or value in an account at the end of a financial period.

Cash Dividend

A payment made by a company out of its profits to its shareholders, usually in the form of cash.

Bonds Payable

Long-term liabilities represented by bonds that a company has issued, which it is obligated to pay back at a future date along with interest payments.

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