Question

2. The highest batting average ever recorded in Major League Baseball was by Ted

Answer 1

Answer:

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.

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

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.