1.1. The random variable $X\textasciitilde{}N( \mu ,{ \sigma }^{2})$. It is known that $P(X>36.88)=0.025$ and $P(X<27.16)=0.1$

Find the values of $a$ and $b$ for which $P(Z>a)=0.025$ and \(P(Z

1.2. Use your answers to part (a), along with the relationship between $Z$ and $X$, to show that the following simultaneous equations must be true:

$\mu +1.96 \sigma =36.88$

$\mu -1.2816 \sigma =27.16$

1.3. By solving the simultaneous equations in (b), determine the values of $\mu$ and $\sigma$. Give your answers correct to 2 decimal places.