Problem

A group of 10 school children are asked to estimate the size of an angle $\theta^\circ$ in a given acute angled triangle. These estimates, in degrees, are as follows.

$84,\ 85,\ 77,\ 85,\ 84,\ 87,\ 86,\ 88,\ 83,\ 85$

(a) Stating any assumptions you make, calculate a $95\%$ confidence interval for $\theta$.

(b) Give a reason why the assumptions made in part (a) may not be appropriate in this case.