The weights of pumpkins on a particular farm are normally distributed with a mean of 13.5 kg and a standard deviation of 3 kg.
A random sample of 15 pumpkins is selected.
Let \(X_1, X_2, X_3, \ldots, X_{15}\) denote the weights of the pumpkins in the sample, and let
\(\overline{X}=\dfrac{X_1+X_2+X_3+\cdots+X_{15}}{15}\).
- Find the expected value of \(\overline{X}.\) (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Find the standard deviation of \(\overline{X}.\) (1 mark)
--- 2 WORK AREA LINES (style=lined) ---