10 The screenshot in Fig. 10 shows the probability distribution for the continuous random variable \(X\), where \(X \sim \mathrm {~N} \left( \mu , \sigma ^ { 2 } \right)\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d8ff9511-aff7-45ea-ba55-e6667e8ba760-06_515_1009_338_529}
\captionsetup{labelformat=empty}
\caption{Fig. 10}
\end{figure}
The area of each of the unshaded regions under the curve is 0.025 . The lower boundary of the shaded region is at 16.452 and the upper boundary of the shaded region is at 21.548 .
- Calculate the value of \(\mu\).
- Calculate the value of \(\sigma ^ { 2 }\).
- \(Y\) is the random variable given by \(Y = 4 X + 5\).
(A) Write down the distribution of \(Y\).
(B) Find \(\mathrm { P } ( \mathrm { Y } > 90 )\).