Question

during the 2019 season, the mean number of wins for major league baseball teams was 81 with a standard deviation of 15.9.
(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 12 standard deviations below 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 0.75 standard deviations above the mean of 81 wins.

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. Here, $x = 93$, $\mu=81$, and $\sigma = 15.9$.

Step2: Substitute values into formula

$z=\frac{93 - 81}{15.9}=\frac{12}{15.9}\approx0.75$

Step3: Interpret z - score

A z - score of $0.75$ means the number of wins of the Washington Nationals (93 wins) is 0.75 standard deviations above the mean number of wins (81 wins) for Major League Baseball teams in 2019.

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.