Respuesta :
Answer:
Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and [tex]11\sqrt2[/tex] respectively.
Step-by-step explanation:
Given that,
For the first 9 holes X:
E(X) = 80
SD(X)=13
For the second 9 holes Y:
E(Y) = 80
SD(Y)=13
For the sum W=X+Y, the following properties holds for means , variance and standard deviation :
E(W)=E(X)+E(Y)
and
V(W)=V(X)+V(Y)
⇒SD²(W)=SD²(X)+SD²(Y) [ Variance = (standard deviation)²]
[tex]\Rightarrow SD(W)=\sqrt{SD^2(X)+SD^2(Y)}[/tex]
∴E(W)=E(X)+E(Y) = 80 +80=160
and
∴[tex]SD(W)=\sqrt{SD^2(X)+SD^2(Y)}[/tex]
[tex]=\sqrt{11^2+11^2}[/tex]
[tex]=\sqrt{2.11^2}[/tex]
[tex]=11\sqrt2[/tex]
Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and [tex]11\sqrt2[/tex] respectively.
