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- 1The following data is from the England and Wales 2011 census Total population: 56 075 912 Number of children aged 5-17: 8 473 617 A random sample of 10 000 peoople in another country was chosen in 2011, and the number, \(m\), of children aged 5-17 was noted. It was found that there was evidence at the 2.5% level that the proportion of children aged 5-16 in the same year was higher than in the UK. unfortunately, when the results were recorded, the value of \(m\) was omitted. Use an appropriate normal distribution to find an estimate of the smallest possible value of \(m\) (5 marks)\(p=0.1511\) to 4sf: B1
\(X~B(10000, 0.1511)\) M1 (seen or implied)
\(np=1511, npq=1283\) M1
\(1511+1.96\times\sqrt{1283} (\mathrm{or} 1511+2\sqrt{1283}\)
\(=1581 \mathrm{or} 1583\) A1ft
Conclusion in context e.g. \(m=1581\) A1 - 2A random variable \(X\) has probability distribution given by \(P(X=x)=\frac{1}{860}(1+x)\) for \(x=1,2,3,...,40\) Given that \(x\) is even, determine \(P(X<10\)\(P(X \mathrm{is even})=\frac{1}{860}(4+(2+4+...+40)\) M1
Simplified expression for sum A1
\(\frac{22}{43}\) A1
\(P(X=2, 4, 6, 8) = \frac{1}{860}(4+(2+4+6+8))\) M1
\(\frac{P(X=2,4,6,8\top X=\mathrm{even})}\)
\(3/55\) B1
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- A level OCR A level Maths Fichas sobre Difficult questions, creado por James Norman el 05/06/2019.
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- James Norman
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