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 when this service life is in control it 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: $$\begin{array} { c c c c c }
\text { Sample } & & { \text { Service Life (hours) } } \
\hline 1 & 495 & 500 & 505 & 500 \
2 & 525 & 515 & 505 & 515 \
3 & 470 & 480 & 460 & 470
\end{array}$$
What is the mean of the sampling distribution of sample means when the service life is in control?
A) 250 hours
B) 470 hours
C) 495 hours
D) 500 hours
E) 515 hours

Question

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 when this service life is in control it 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: $$\begin{array} { c c c c c } 
\text { Sample } & & { \text { Service Life (hours) } } \
\hline 1 & 495 & 500 & 505 & 500 \
2 & 525 & 515 & 505 & 515 \
3 & 470 & 480 & 460 & 470
\end{array}$$
What is the mean of the sampling distribution of sample means when the service life is in control?
A) 250 hours
B) 470 hours
C) 495 hours
D) 500 hours
E) 515 hours

Quizplus · Accepted Answer

The mean of the sampling distribution of sample means can be calculated using the formula:

$\mu_{\bar{x}} = \mu = 500$

where $\mu_{\bar{x}}$ is the mean of the sampling distribution of sample means and $\mu$ is the population mean.

Therefore, the mean of the sampling distribution of sample means when the service life is in control is 500 hours. The correct choice is (D).

A Design Engineer Wants to Construct a Sample Mean Chart