$2\mathrm{.}1$ Create a t$-$distribution table in Excel and submit it as part of your assignment.

Using the table $($or Excel functions$),$ answer the following question.

$2\mathrm{.}2$ A cattle farmer regularly weighs a random sample of his cattle in order to determine their readiness for market. He has a big herd and can only weigh $20$ cattle each week. The results from this week's weighing are as follows $($in kg$)$:

$487490466485472$

$457492483495458$

$468462460499477$

$482497453482484$

On the basis of these results the farmer concludes that his herd has reached the required average market readiness weight of $480$kg$.$ Do you agree with him? What if the readiness weight is $485$kg$?$ State any assumptions.