An IP school has $2000$ students – there are $200$ students in each level from Secondary 1-

Question

An IP school has $2000$ students – there are $200$ students in each level from Secondary 1-4, $600$ in JC1 and $600$ in JC2. The Student Council is interested in finding $x$ hours, the amount of time each student spends in a week doing homework. The president of the Student Council thus decides to survey $50$ students. The data gathered is summarised as follows: $\sum{x}=600$; $\sum{{{x}^{2}}}=7300$ Calculate the unbiased estimates of the population mean and variance. Given that $\mu $=12, find the probability that the sample mean exceeds $12.1$.

Accepted Answer

(i) $\bar x=12,\ s^2=\frac{100}{49}$ (ii) $0.310\text{ (3 s.f.)}$

2012 NJC Q10 [Modified]

2012 NJC Q10 [Modified]

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