The time needed for checking in at a motel is to be investigated. Historically, the process has had a standard deviation equal to $0\mathrm{.}139$ The means of $39$ samples of $\backslash ($ n$=16\backslash )$ are a$-1.$ Construct an $\backslash (\backslash$bar$\{$x$\}\backslash )-$chart for this process with three$-$sigma limits$.$

Note: Do not round intermediate calculations. Round your answers to $2$ decimal places.

a$-2.$ Is the process in control?

Yes

No

b$.$ Analyze the data using a median run test and an up or down run test. What can you conclude?