To determine whether a braking system meets specification, a random sample of $10$ brake systems were tested. The sample mean and sample variance of the braking distance were found to be $233\mathrm{.}3$ cm and $95\mathrm{.}64$ respectively. Suppose the design target is that the mean braking distance should not be longer than $250$ cm$.($Note: confidence level at $99\%)$

$($a$)$ If you are a costomer$,$ what is your major concern? Pleaes check if your concern is addressed with the available date?

$($b$)$ If you are an engineer, what is your major concern? Please check if your concern is addressed with the available data.

$($c$)$ Comments on your results of a$)$ and b$)$ about: $1)$ Are there any difference? $2)$ How to improve the test results?

$($d$)$ List all the assumptions in your tests