Question

In 2012, the mean number of wins for teams in Major League Baseball was 81 with a standard deviation of 11.9 wins. Find and interpret the Z-scores for the New York Yankees, with 95 wins.

Answer 1

The Z-score for the New York Yankees with 95 wins in 2012 is approximately 1.18; this signifies that their number of wins is 1.18 standard deviations above the mean for Major League Baseball that year.

Step-by-step explanation:

The Z-score is a measure of how far away a data point is from the mean, measured in terms of standard deviations. To find the Z-score for the New York Yankees with 95 wins, we need to use the formula: Z = (X - µ) / σ, where X is the number of wins, µ is the mean number of wins, and σ is the standard deviation. In this case, the mean (µ) is 81 wins, and the standard deviation (σ) is 11.9 wins.

Calculating the Z-score: Z = (95 - 81) / 11.9 = 14 / 11.9 ≈ 1.18.

The Z-score of 1.18 means that the New York Yankees' 95 wins are 1.18 standard deviations above the mean number of wins in Major League Baseball for 2012.