Question

during the 2019 season, the mean number of wins for major league baseball teams was 81 with a standard deviation of 15.9 wins.
(a) find the standardized score (z - score) for the washington nationals, who won 93 games (and the world series!).

z = (round to 2 decimal places.)

(b) interpret the z - score you found in part (a).
the washington nationals number of wins in 2019 is 12 games above the mean of 81 wins.
the washington nationals number of wins in 2019 is 0.75 standard deviations below the mean of 81 wins.
the washington nationals number of wins in 2019 is 12 standard deviations below the mean of 81 wins.
the washington nationals number of wins in 2019 is 0.75 standard deviations above the mean of 81 wins.

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $\mu = 81$, $\sigma=15.9$, and $x = 93$.

Step3: Calculate z - score

Substitute the values into the formula: $z=\frac{93 - 81}{15.9}=\frac{12}{15.9}\approx0.75$.

Step4: Interpret z - score

A positive z - score indicates that the data - point is above the mean. The value of the z - score represents the number of standard deviations the data - point is from the mean. Since $z\approx0.75$, the Washington Nationals' number of wins in 2019 is 0.75 standard deviations above the mean of 81 wins.

Answer:

(a) $z\approx0.75$
(b) The Washington Nationals number of wins in 2019 is 0.75 standard deviations above the mean of 81 wins.