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.

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

(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.