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\includegraphics[max width=\textwidth, alt={}, center]{1a10471c-5810-44ca-9353-c2c76e190a2b-2_542_876_1425_632}
The random variable \(X\) has a normal distribution with mean 4.5. It is given that \(\mathrm { P } ( X > 5.5 ) = 0.0465\) (see diagram).
- Find the standard deviation of \(X\).
- Find the probability that a random observation of \(X\) lies between 3.8 and 4.8.