Hi I was wondering about the following problem:
If there are $1000$ students in a school and the combined scores of these students over the last $5$ years are $5823, 6107, 5672, 6233$ and $5598$ respectively. What is the estimated number of students who this year score between $10$ and $20$.
I am unsure how to approach this solution and specifically unsure whether to use the random variable $X$ as the random variable for the combined score or the individual score. For example if $X$ is the combined scores then I could take $\hat{\mu}=\frac{1}{5}\sum \frac{X}{1000}$ then calculate the variance in a similar manner before applying this to the formula:
$$ P ( 10 < X < 20 ) \\ P\bigg( \frac{10-\hat{\mu}}{\frac{\hat{\sigma}}{\sqrt{N}}}< Z < ..\bigg) $$
Then upon calulating this probabiltiy I could simply multiply it by 1000 to get the estimated number of players in that range.
Any advice would be appreciated, even if not particular to this problem.
Thanks.