3 The weight, \(X\) grams, of talcum powder in a tin may be modelled by a normal distribution with mean 253 and standard deviation \(\sigma\).
- Given that \(\sigma = 5\), determine:
- \(\mathrm { P } ( X < 250 )\);
- \(\mathrm { P } ( 245 < X < 250 )\);
- \(\mathrm { P } ( X = 245 )\).
- Assuming that the value of the mean remains unchanged, determine the value of \(\sigma\) necessary to ensure that \(98 \%\) of tins contain more than 245 grams of talcum powder.
(4 marks)
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