A local community college recently took two random sample of grade point averages of its graduating.

A local community college recently took two random sample
of grade point averages of its graduating students. To check the consistency of
the teachers' grading policies, it needs an estimate of the variance σ^{2}
and standard deviation σ.

(a). If N = 30 and s^{2 }= 0.3, estimate the
variance σ^{2} and standard deviation σ of the grade point
average using a confidence interval of 90%.

(b). If N = 200 and s^{2} = 0.18, estimate the
variance σ^{2} and standard deviation σ of the grade point
average using a confidence interval of 90%.