1. For the random variable $X\textasciitilde{}N( \mu ,36)$ it is known that $P(X<51)=0.8665$.

(i) Write down the value of $\sigma$.

(ii)Calculate the value of $z$ such that P(Z</p><p style="line-height: 1.7" class="text-lg tracking-wide font-normal leading-relaxed">(iii)Use the formula \(Z=\frac{X- \mu }{ \sigma } to show that $51- \mu =6.66$.

(iv) Hence calculate the value of $\mu$.