Help with C.I. for non normal probability distribution Excercise

#1
Hi! first time poster here!

I have done (correctly I hope) most of the exercise except for segment "B) i)" So I need help with it :(:(

Here's the exercise


[What I've got so far]
n = 10
A) sample mean (x) = 5.7 ; Std Deviation = 3.257
B) ii) Error = 2.0143 ; U € [3.685 ; 7.714] 95

My first guess was to use formula (FIG 1.1) for parameters of non-normal distributons but it needs a sample size bigger then 30 (n >=30) because it relies on the bias-corrected std deviation (S1) being asymptotically unbiased and in the C.L.T.

FIG 1.1


Maybe there's no way of doing it and the purposse is to make me realize the importance of a bigger n for asymptotically unbiased estimators and the precision of the C.I. Should I just use FIG 1.1 and write the rationale comenting on the big error and all that?

Solution with FIG 1.1:
Error = 2.1259 ; U € [3.574 ; 7.8459] 95