2 A garden centre sells bamboo canes of nominal length 1.8 metres. The length, \(X\) metres, of the canes can be modelled by a normal distribution with mean 1.86 and standard deviation \(\sigma\).
- Assuming that \(\sigma = 0.04\), determine:
- \(\mathrm { P } ( X < 1.90 )\);
- \(\mathrm { P } ( X > 1.80 )\);
- \(\mathrm { P } ( 1.80 < X < 1.90 )\);
- \(\mathrm { P } ( X \neq 1.86 )\).
- It is subsequently found that \(\mathrm { P } ( X > 1.80 ) = 0.98\).
Determine the value of \(\sigma\).
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