Answer:
<u>Ted Williams had a better year relative to his peers because the z-score and percentage of his batting average in 1941 are higher than Jose Altuve's z-score and percentage in 2014. </u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Ted Williams batting average in 1941 = 0.406
Mean of batting average in 1941 = 0.2806
Standard deviation of batting average in 1941 = 0.0328
Jose Altuve batting average in 2014 = 0.341
Mean of batting average in 1941 = 0.2679
Standard deviation of batting average in 1941 = 0.0282
2. Who had the better year relative to his peers, Williams or Altuve? Why?
Assuming a normal distribution for the batting average in Major League Baseball, we need to calculate the z-score to find out who had the better year relative to his peers, this way:
z-score Ted Williams = (0.406 - 0.2806)/0.0328
z-score Ted Williams = 0.1254/0.0328
z-score Ted Williams = 3.82
P for this z-score = 0.99993
z-score Jose Altuve = (0.341 - 0.2679)/0.0282
z-score Ted Williams = 0.0731/0.0282
z-score Ted Williams = 2.59
P for this z-score = 0.99520
3.82 > 2.59
<u>Ted Williams had a better year relative to his peers because the z-score and percentage of his batting average in 1941 are higher than Jose Altuve's z-score and percentage in 2014. </u>
