(Solved): (In solving the questions, you may or may not need to use the standard normal table posted in Canva ...

(In solving the questions, you may or may not need to use the standard normal table posted in Canvas. Recall that by the symmetry of standard normal distribution, we have for any $t?\mathbf{R}$, $\begin{array}{rl}P\{Z?t\}& =P\{?Z?t\}\\ & =P\{Z??t\}.\end{array}$ Try to visualize this by thinking about the tail areas of the standard normal density function.) (ii) (G) Find $\mathrm{Var}\left(\frac{1}{\sqrt{n}}{?}_{i=1}^{n}1\left\{X_i?6\right\}\right).$ (iii) Let us define two random variables: $Z=1\left\{X_1+X_2+X_3?18\right\}\text{ and }W=1\left\{X_4+X_5?12\right\}\text{. }$ Compute the following probability: (iv) (G) For each $i=1,\dots ,n$, define a random variable $Y_i$ as follows: $Y_i=1\left\{X_i?1\right\}$