Show me the steps to solve: $15-16$ 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:

What is the overall average of these means? What is the average range?

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

Does this process appear to be in control? Explain.

The table has $11$ columns and $2$ rows. The column headers are: sample; $1$; $2$; $3$; $4$; $5$; $6$; $7$; $8$; $9$; $10.$ The row entries from left to right are as follows: Row $1$: mean, $979,1,087,1,080,934,1,072,1,007,952,986,1,063,958.$ Row $2$: range, $50,94,57,65,135,134,101,98,145,84.$

$[$QX$]15-17$ For Problem $15-16,$ develop upper and lower control limits for the range. Do these samples indicate that the process is in control?