A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 86 with a standard deviation of 8. 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?

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haseebee12 haseebee12 · Answer 1 · 2019-12-12T06:08:59+01:00

Answer:

The mean of his total score if the golfer plays a full 18 holes is 172 and standard deviation is 11.3

Explanation:

Given data:

For the first nine holes:

For the second nine holes:

We know that

For the two independent numbers A and B, the sum of mean of these numbers is equal to the mean of a number C.

Mean of A + Mean of B = Mean of C

Applying this to our situation, we get:

Mean for 1st half 9 holes + Mean for 2nd half 9 holes = Mean for full 18 holes

Rearranging the above equation

Mean of score for full 18 holes = Mean of score for 1st half 9 holes + Mean of score for 2nd half 9 holes

Putting the values of mean in above equation we get,

Mean of score full 18 holes = 86 + 86

Mean of score full 18 holes = 172

Now for standard deviation, the same property applies,

For the two independent numbers A and B, the sum of standard deviation these numbers is equal to the standard deviation of a number C.

Standard deviation of C =

[tex]\sqrt{(Standard deviation of A)² + (Standard deviation of B)² } \[/tex]

Applying this to our situation and replacing Standard deviation with SD,

SD of score for full holes = [tex]\sqrt{(SD of 1st half)² + (Standard deviation of 2nd half)² } \[/tex]

SD of score for full holes = [tex]\sqrt{(8)² + (8)²}\\[/tex]

SD of score for full holes = [tex]\sqrt{128\\}[/tex]

SD of score for full holes = 11.3