A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 8080 with a standard deviation of 1313. Assuming that the second 9 has the same mean and standard deviation, what are the mean and standard deviation of his total score if he plays a full 18 holes?

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]

∴E(W)=E(X)+E(Y) = 80 +80=160

            and

∴

Therefore the mean and standard deviation of his total score if he plays a full 18 holes are 160 and respectively.

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step-by-step explanation: