Ans: (a) (i) $\dfrac{3}{5}$ (ii) (1) $\dfrac{4}{21}$ (2) $\dfrac{419}{630}$ (b) (i) Median $=\$5\ 000$, inter-quartile range $=\$2\ 100$ (ii) Extra $\$1\ 000$ can be given to each of the $36$ salesgirls.
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- The required probability
$\begin{array}{cl}
= & \dfrac{9}{15} \\
= & \dfrac{3}{5}
\end{array}$ -
- The required probability
$\begin{array}{cl}
= & \dfrac{8}{36} \times \dfrac{15}{35} + \dfrac{15}{36} \times \dfrac{8}{35} \\
= & \dfrac{4}{21}
\end{array}$ - The required probability
$\begin{array}{cl}
= & 1 – \dfrac{8}{36} \times \dfrac{7}{35} – \dfrac{15}{36} \times \dfrac{14}{36} – \dfrac{13}{36} \times \dfrac{12}{35} \\
= & \dfrac{419}{630}
\end{array}$
- The required probability
- The required probability
-
- The median
$\begin{array}{cl}
= & \dfrac{5000 + 5000}{2} \\
= & \$5~000
\end{array}$The lower quartile
$\begin{array}{cl}
= & \dfrac{4300+4300}{2} \\
= & \$ 4~300
\end{array}$The upper quartile
$\begin{array}{cl}
= & \dfrac{6400 + 6400}{2} \\
= & \$6~400
\end{array}$Therefore, the inter-quartile range
$\begin{array}{cl}
= & 6400 – 4300 \\
= & \$2~100
\end{array}$ - For increasing the median $20\%$, then all bonuses should be $\$1~000$ for each salesgirls or $20\%$ of their own salary. For the inter-quartile range remaining unchanged, then all bonuses should be increased by the same amount. Therefore, the manager should give $\$1~000$ to each of the $36$ salesgirls.
- The median
