Answer:
Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and
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]
![\Rightarrow SD(W)=\sqrt{SD^2(X)+SD^2(Y)}](https://tex.z-dn.net/?f=%5CRightarrow%20SD%28W%29%3D%5Csqrt%7BSD%5E2%28X%29%2BSD%5E2%28Y%29%7D)
∴E(W)=E(X)+E(Y) = 80 +80=160
and
∴![SD(W)=\sqrt{SD^2(X)+SD^2(Y)}](https://tex.z-dn.net/?f=SD%28W%29%3D%5Csqrt%7BSD%5E2%28X%29%2BSD%5E2%28Y%29%7D)
![=\sqrt{11^2+11^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B11%5E2%2B11%5E2%7D)
![=\sqrt{2.11^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B2.11%5E2%7D)
![=11\sqrt2](https://tex.z-dn.net/?f=%3D11%5Csqrt2)
Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and
respectively.