In the average ball game, the sum of the scores of both teams is 4545, with a standard deviation of 55. If the score of a game resulted in a z-score of 1.801.80 and the winning team had a score of 3333, what was the other team's score?
To find the other team's score, we need to calculate the z-score of their score and then use the formula for z-score to find the corresponding raw score.
A z-score measures how many standard deviations an individual score is from the mean. The formula for calculating the z-score is:
z = (X - μ) / σ
Where:
- "z" is the z-score
- "X" is the individual score
- "μ" is the mean score
- "σ" is the standard deviation
In this case, the winning team's score of 3333 is given, and we know the z-score is 1.80. To find the other team's score, we'll rearrange the formula and solve for "X":
X = (z * σ) + μ
First, we need to find the mean μ by subtracting the winning team score from the sum of both teams' scores:
μ = (4545 - 3333) / 2 = 1212
Next, we can substitute the values into the equation:
X = (1.80 * 55) + 1212
X = 99 + 1212
X = 1311
Therefore, the other team's score is 1311.