A Design Engineer Wants to Construct a Sample Mean Chart

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: $$\begin{array} { r } { \text { Service Life (hours) } }\\\begin{array} { l l l l l } \text { Sample } & \\\hline 1 & 495 & 500 & 505 & 500 \\2 & 525 & 515 & 505 & 515 \\3 & 470 & 480 & 460 & 470\end{array}\end{array}$$ 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