Question: Suppose that X has a distribution such that \(\mu =100\) and \(\sigma =48\).

(a) If a random sample of size n = 81 is drawn, find \({{\mu }_{{\bar{X}}}}\), \({{\sigma }_{{\bar{x}}}}\) and \(\Pr \left( 92\le \bar{X}\le 100 \right)\)

(b) If a random sample of size n = 121 is now drawn, find \({{\mu }_{{\bar{X}}}}\), \({{\sigma }_{{\bar{x}}}}\) and \(\Pr \left( 92\le \bar{X}\le 100 \right)\)

(c) Comment on the difference found in (a) and (b).