Question

one season, baseball player a hit 50 home runs. during a different season, baseball player b hit 64 home runs. how does the performance of player a compare to the performance of player b? the table available below shows the means and standard deviations for the number of home runs scored by all players with at least 502 plate appearances in their respective seasons. use these to determine whose home - run feat was more impressive. means and standard deviations for the two seasons

	mean	standard deviation
season with player b	23.6	13.42

print
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Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. We want to compare how many standard - deviations each player's home - run count is from the mean. For player A, $\mu_A = 21.6$ and $\sigma_A=12.72$, and $x_A = 50$. For player B, $\mu_B = 23.6$ and $\sigma_B = 13.42$, and $x_B=64$.

Step2: Calculate z - score for player A

$z_A=\frac{x_A-\mu_A}{\sigma_A}=\frac{50 - 21.6}{12.72}=\frac{28.4}{12.72}\approx2.23$

Step3: Calculate z - score for player B

$z_B=\frac{x_B-\mu_B}{\sigma_B}=\frac{64 - 23.6}{13.42}=\frac{40.4}{13.42}\approx3.01$

Since $z_B>z_A$, player B's home - run performance is more impressive relative to the mean of players with at least 50 plate appearances in their respective seasons.

Answer:

Player B's performance is more impressive as their z - score (approximately 3.01) is higher than player A's z - score (approximately 2.23).