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Determine the probability that the mean, $\bar{F}$, of the final marks for a random sample of $25$ candidates exceeds $143$.
Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
In a particular diploma, candidates sit two tests. Their first-test and second-test marks are represented by independent variables with distributions $N(38.1, 3.8^2)$ and $N(64.0, 6.1^2)$ respectively. The final mark, $F$, for each candidate is obtained by doubling the first-test mark and then adding that to the second-test mark.