15 A fair dice is thrown 1000 times and the number, \(X\), of throws on which the score is 6 is noted.
- State the distribution of \(X\).
- Explain why a normal distribution would be an appropriate approximation to the distribution of \(X\).
- Use a normal distribution to find two positive integer values, \(a\) and \(b\), such that \(\mathrm { P } ( a < X < b ) \approx 0.4\).
- For your two values of \(a\) and \(b\), use the distribution of part (a)(i) to find the value of \(\mathrm { P } ( a < X < b )\), correct to 3 significant figures.
\section*{OCR}
Oxford Cambridge and RSA