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.

TransEx has been hired to move the lightbulbs to retail stores. The network of roads is

shown in the figure below. The distances are given in hundreds of km $.$

d$)$ What route that provides the shortest way? Draw the network and describe the

route selection.

e$)$ What is the total shortest distance?