Question $5$

$($Total: $20$ marks$)$

Vivid Electric is a company that produces lightbulbs and other electrical products. One

lightbulb should have an average life of about $1,000$ hours before it burns out.

Periodically, the company will test $10$ bulbs and measure the average time before they

burn out. The following table gives the results of $20$ such samples.

a$)$ What is the overall average of the mean and average range?

b$)$ What are the upper and lower control limit for a $99\mathrm{.}7\%$ control chart for the mean?

c$)$ Does the process appear to be in control? Explain in detail.