Question

A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 85 with a standard deviation of $11 .$ Assuming that the second 9 has the same mean and standard deviation, what is the mean and standard deviation of his total score if he plays a full 18 holes?

Name: Problem 34, Chapter 15: Stats Modeling the World 4th
Uploaded: 2022-11-09T13:29:27-08:00
Duration: 1 min 11 s
Channel: Kari Hasz
Description: A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 85 with a standard deviation of 11 . Assuming that the second 9 has the same mean and standard deviation, what is the mean and standard deviation of his total score if he plays a full 18 holes?

   A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 85 with a standard deviation of $11 .$ Assuming that the second 9 has the same mean and standard deviation, what is the mean and standard deviation of his total score if he plays a full 18 holes?

Stats Modeling the World 4th

David E. Bock, Paul… 4th Edition

Chapter 15, Problem 34

Instant Answer

Solved by Expert Kari Hasz

11/09/2022

Step 1

Since the mean score for playing 9 holes is 85, the mean score for playing 18 holes would be double that, which is 170. Now, let's find the standard deviation for playing 18 holes. Since the golfer's scores are assumed to be independent, we can use the formula Show more…

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A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 85 with a standard deviation of $11 .$ Assuming that the second 9 has the same mean and standard deviation, what is the mean and standard deviation of his total score if he plays a full 18 holes?

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Key Concepts

Mean (Expected Value)

The mean, or expected value, of a random variable is a measure of its central tendency. When dealing with the sum of independent random variables, the overall mean is simply the sum of the individual means.

Variance and Standard Deviation in Sums

Variance quantifies the spread of a distribution, and the standard deviation is the square root of the variance. For independent random variables, the variance of the total is the sum of the individual variances, and thus the standard deviation of the total is the square root of that sum.

Independence of Random Variables

Independence means that the outcomes of one variable do not influence the outcomes of another. This property is crucial because it allows for the additive property of variances, thereby simplifying the calculation of the overall variance and standard deviation for the sum of independent variables.

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