Question

A six-sided and a ten-sided die are both rolled. The mean and S.D. for the six-sided die are $3.5$ and $1.707$. For the ten-sided die, the mean and S.D. are $5.5$ and $2.872$. Find the combine variance if the results of the two dice are added.

• A. $3.67$
• B. $3.341$
• C. $2.89$
• D. None of htese

Answer 1

The correct option is D None of htese

For dice with $n=6$

$X_1=3.5,{\sigma }_1=1.707$

For dice with $n=10$

$X_2=5.5,{\sigma }_2=2.872$

$X_c=\frac{n_1{X}_1+n_2{X}_2}{n_1+n_2}{X}_c=\frac{6\times 3.5+10\times 5.5}{6+10}=4.75$

$d_1=X_1-X_c=3.5-4.75=-1.25d_2=X_2-X_c=5.5-4.75=.75$

Variance of combined data is

${\sigma }^2=\frac{n_1(d_1^2+{\sigma }_1^2)+n_2(d_2^2+{\sigma }_2^2)}{n_1+n_2}$

${\sigma }^2=\frac{6\{{(-1.25)}^2+{\left(1.707\right)}^2\}+10\{{\left(.75\right)}^2+{\left(2.872\right)}^2\}}{6+10}$

${\sigma }^2=7.1854$

So, the variance is $7.1854$.

Hence, option D is correct.