2 Henri wants to choose a random sample from the 804 students at his college. He numbers the students from 1 to 804 and then uses random numbers generated by his calculator. The first 20 random digits produced by his calculator are as follows.
$$\begin{array} { l l l l l l l l l l l l l l l l l l l l }
5 & 6 & 7 & 1 & 0 & 9 & 8 & 4 & 3 & 1 & 0 & 9 & 6 & 6 & 5 & 0 & 2 & 1 & 7 & 6
\end{array}$$
Henri's first two student numbers are 567 and 109.
- Use Henri's digits to find the numbers of the next two students in the sample.
There were 30 students in Henri's sample. He asked each of them how much time, \(X\) hours, they spent on social media each week, on average. He summarised the results as follows.
$$n = 30 \quad \Sigma x = 610 \quad \Sigma x ^ { 2 } = 12405$$ - Use this information to calculate an unbiased estimate of the mean of \(X\) and show that an unbiased estimate of the variance of \(X\) is less than 0.1 .
- Henri's friend claims that Henri has probably made a mistake in his calculation of \(\Sigma x\) or \(\Sigma x ^ { 2 }\).
Use your answer to part (b) to comment on this claim.