3. The random variable \(X \sim \mathrm {~N} \left( \mu , \sigma ^ { 2 } \right)\).
It is known that
$$\mathrm { P } ( X \leq 66 ) = 0.0359 \text { and } \mathrm { P } ( X \geq 81 ) = 0.1151 .$$
- In the space below, give a clearly labelled sketch to represent these probabilities on a Normal curve.
- Show that the value of \(\sigma\) is 5 .
- Find the value of \(\mu\).
- Find \(\mathrm { P } ( 69 \leq X \leq 83 )\).