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[Steps Shown] Let Z_1, Z_2, ..., Z_16 be an independent random sample of size 16 from N(0,1), and let Y_1, Y_2, ..., Y_64 be another independent random

Question: Let $Z_{1}, Z_{2}, \ldots, Z_{16}$ be an independent random sample of size 16 from $N(0,1)$, and let $Y_{1}, Y_{2}, \ldots, Y_{64}$ be another independent random sample of size 64 from $N(\mu, 1)$ and The two samples are independent.

Find $P\left(Z_{1}>2\right)$
Find $P\left(\sum_{i=1}^{16} Z_{i}>2\right)$
Find $P\left(\sum_{i=1}^{16} Z_{i}^{2}>6.91\right)$
Let $S_{Z}^{2}$ and $S_{Y}^{2}$ be the sample variances of $Z$ and $Y$ respectively.

Find $\mathrm{c}$ such that $P\left(S_{Y}^{2}>c\right)=0.05$

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[Steps Shown] Let Z_1, Z_2, ..., Z_16 be an independent random sample of size 16 from N(0,1), and let Y_1, Y_2, ..., Y_64 be another independent random

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