3 Many types of computer have cooling fans. The random variable \(X\) represents the lifetime in hours of a particular model of cooling fan. \(X\) is Normally distributed with mean 50600 and standard deviation 3400.

1. Find \(\mathrm { P } ( 50000 < X < 55000 )\).
2. The manufacturers claim that at least \(95 \%\) of these fans last longer than 45000 hours. Is this claim valid?
3. Find the value of \(h\) for which \(99.9 \%\) of these fans last \(h\) hours or more.
4. The random variable \(Y\) represents the lifetime in hours of a different model of cooling fan. \(Y\) is Normally distributed with mean \(\mu\) and standard deviation \(\sigma\). It is known that \(\mathrm { P } ( Y < 60000 ) = 0.6\) and \(\mathrm { P } ( Y > 50000 ) = 0.9\). Find the values of \(\mu\) and \(\sigma\).
5. Sketch the distributions of lifetimes for both types of cooling fan on a single diagram.