Answer:
8.15 or 163/20 or 8 3/20
Explanation:
The expected value of a random variable can be determined by the below formula;
[tex]\mu=\Sigma x\ast p(x)[/tex]
where
[tex]\begin{gathered} \mu=\text{ Expected value ( Mean)} \\ x=given\text{ scores} \\ p(x)=the\text{ probability} \end{gathered}[/tex]
So all we need to do is multiply each of the given score values by their respective probability values and find the sum as shown below;
[tex]\mu=(0\ast0.1)+(6\ast0.05)+(7\ast0.35)+(10\ast0.2)+(11\ast0.2)+(12\ast0.1)_{}[/tex][tex]\mu=0+0.3+2.45+2+2.2+1.2[/tex][tex]\mu=8.15[/tex]
We can also express our answer as a fraction as shown below;
[tex]\frac{8.15}{1}=\frac{815}{100}=\frac{163}{20}=8\frac{3}{20}[/tex]
