(a)[2]
State the distribution of $\bar{H}$, and include the values of any parameters.
(b)[3]
Find the value of $P(12 < \bar{H} < 13)$.
Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
The height $H$, measured in metres, of trees of one kind is distributed as $N(12.5, 10.24)$. A scientist selects a random sample of 25 trees of this kind and calculates the sample mean, $\bar{H}$, of their heights.