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 = \boxed{\space} (round to 2 decimal places.)
(b) interpret the z-score you found in part (a).
\bigcirc the washington nationals number of wins in 2019 is 12 standard deviations below the mean of 81 wins.
\bigcirc the washington nationals number of wins in 2019 is 12 games above the mean of 81 wins.
\bigcirc the washington nationals number of wins in 2019 is 0.75 standard deviations above the mean of 81 wins.
\bigcirc the washington nationals number of wins in 2019 is 0.75 standard deviations below the mean of 81 wins.

Explanation:

Part (a)

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the dataset, $\mu$ is the mean, and $\sigma$ is the standard deviation.
Here, $x = 93$ (number of wins for Washington Nationals), $\mu=81$ (mean number of wins), and $\sigma = 15.9$ (standard deviation of number of wins).

Step2: Substitute values into formula

Substitute $x = 93$, $\mu=81$, and $\sigma=15.9$ into the z - score formula:
$z=\frac{93 - 81}{15.9}$
First, calculate the numerator: $93-81 = 12$.
Then, divide by the standard deviation: $z=\frac{12}{15.9}\approx0.75$ (rounded to two decimal places).

The z - score of a value tells us how many standard deviations the value is above or below the mean. A positive z - score means the value is above the mean. We found the z - score to be approximately 0.75, so we interpret this as the Washington Nationals' number of wins in 2019 is 0.75 standard deviations above the mean of 81 wins.

Answer:

$0.75$

Part (b)