two golfers plan to enter a tournament where the score will be determined as a team score. golfer x has a mean score of 85.4 and St. Deviation of 3.2 while golfer y has a mean score of 89.6 and St. deviation of 4.1. what is their expected team score and the variation associated with it?
To find the expected team score, we need to add the mean scores of golfer X and golfer Y.
Mean score of golfer X = 85.4
Mean score of golfer Y = 89.6
Expected team score = Mean score of golfer X + Mean score of golfer Y
= 85.4 + 89.6
= 175
So, their expected team score is 175.
To find the variation associated with the team score, we need to find the standard deviation of the team scores. Since the scores are independent, we can use the formula:
Standard deviation of the sum of independent random variables = square root of (sum of the variances)
Variance of golfer X = (St. Deviation of X)^2 = (3.2)^2 = 10.24
Variance of golfer Y = (St. Deviation of Y)^2 = (4.1)^2 = 16.81
Variance of the team score = Variance of golfer X + Variance of golfer Y
= 10.24 + 16.81
= 27.05
So, the variation associated with the team score is 27.05.
To find the expected team score and the variation associated with it, we need to consider the mean scores and standard deviations of the two golfers.
First, let's calculate the expected team score by adding the mean scores of Golfer X and Golfer Y. Golfer X's mean score is 85.4, and Golfer Y's mean score is 89.6. So, the expected team score is:
Expected Team Score = Mean score of Golfer X + Mean score of Golfer Y
= 85.4 + 89.6
= 175
Now, let's calculate the variation associated with the team score. Since this is a team score, we need to consider the variation of both golfers. When combining two independent random variables, the variances add up.
The variance of Golfer X is the square of the standard deviation, which is (3.2)^2 = 10.24.
The variance of Golfer Y is the square of the standard deviation, which is (4.1)^2 = 16.81.
To find the variance of the team score, we add these variances together:
Variance of Team Score = Variance of Golfer X + Variance of Golfer Y
= 10.24 + 16.81
= 27.05
Finally, we can calculate the standard deviation of the team score by taking the square root of the variance:
Standard Deviation of Team Score = √Variance of Team Score
= √27.05
≈ 5.20
Therefore, the expected team score is 175 and the associated variation (standard deviation) is approximately 5.20.