$[$QX$]$: $15-16$ Colonel Electric is a large company that produces lightbulbs and other electrical

products. One particular lightbulb is supposed to have an average life of about $1,000$ hours before it

burns out. Periodically, the company will test five of these and measure the average time before

these burn out. The following table gives the results of $10$ such samples:

a$.$ What is the overall average of these means? What is the average range?

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

c$.$ Does this process appear to be in control? Explain.