a) $z = 0.807$

$0.807 = \frac{{10 - 8.2}}{\sigma }$

$s = 2.23$

b) $P$($ \gt 1$ min from mean) $ = P$(mod $z \gt \frac{1}{{2.23}}$)

$ = P\left( {\left| z \right| \gt 0.4484} \right)$

$ = \left( {1 - 0.6729} \right) \times 2$

$ = 0.654$

c) $P$($ \gt 2$ longer) $ = 1 - P$($0$, $1$, $2$ longer)

$ = 1 - \{ {\left( {0.79} \right)^6} + {}^6{C_1}\left( {0.21} \right)\left( {0.79} \right)5 + $

${}^6{C_2}{\left( {0.21} \right)^2}{\left( {0.79} \right)^4}\} $

$ = 0.112$

d) $\mu  = 35 \times 0.5 = 17.5$

${\sigma ^2} = 35 \times 0.5 \times 0.5 = 8.75$

$P\left( {X \lt 16} \right) = \Phi \left( {\frac{{15.5 - 17.5}}{{\sqrt {8.75} }}} \right)$

$ = 1 - \Phi \left( {0.676} \right)$

$ = 1 - 0.7505$

$ = 0.2495{\text{ }}\left( {0.249{\text{ }}or{\text{ }}0.250} \right)$

OR ${}^{35}{C_0}{0.5^0}{0.5^{35}} + {}^{35}{C_1}{0.5^1}{0.5^{34}} + {}^{35}{C_2}{0.5^2}{0.5^{33}} + ...$

$ = 8582372584/{2^{35}} = 0.250$