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:

Temporary Accounts

Accounts in financial accounting that are closed at the end of each accounting period, including income, expense, and withdrawal accounts. They are used to track transactions within a specific period and are reset to zero at the start of a new period to begin tracking new transactions.

Total Debits

The sum of all debit entries in a financial account or ledger, representing expenses or assets.

Closing Process

The procedure used in accounting to close out accounts at the end of an accounting period, summarizing revenues and expenses and showing net income or loss.

Income Summary

An account to which all income statement account balances are transferred at the end of an accounting period to determine the net profit or loss.