2. The random variable \(X\) is normally distributed with mean 177.0 and standard deviation 6.4.
- Find \(\mathrm { P } ( 166 < X < 185 )\).
It is suggested that \(X\) might be a suitable random variable to model the height, in cm , of adult males.
- Give two reasons why this is a sensible suggestion.
- Explain briefly why mathematical models can help to improve our understanding of real-world problems.