An IT company develops different Software packages that are downloadable from their servers on the internet. They need to make sure the download speed of their servers is as planned and adjust the capacity of their servers anytime needed. They measure the download time of their software $6$ times a day for $5$ days as shown in the table below. The standard deviation of the download time is $6\mathrm{.}78.$

$\backslash$table$[[$Download time in seconds$],[$Day $1,$Day $2,$Day $3,$Day $4,$Day $5],[51,33,35,32,45],[40,37,42,52,37],[34,39,37,45,54],[49,37,52,47,51],[42,46,41,37,39],[50,45,31,51,50]]$

a$.$ Construct an appropriate control chart $($with two$-$sigma limits$)$ to demonstrate if the download time is within the company's expectation and the process is in control. $($Round your answer to two decimal places.$)$

$\backslash$table$[[,],[$UCL of $\stackrel{}{x},],[$LCL of $\stackrel{}{x},]]$

b$.$ Do you think the download time on any of these days had a wide range? Use a control chart to support your answer. $($Round your answer to two decimal places.$)$