Question

the table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell - shaped. compare the z - scores for the actors in the following situation.
best actor\tbest supporting actor
μ = 45.0\tμ = 49.0
sigma = 9.6\tsigma = 16
in a particular year, the best actor was 54 years old and the best supporting actor was 45 years old.
determine the z - scores for each.
best actor: z=
best supporting actor: z=
(round to two decimal places as needed.)

Explanation:

Step1: Recall z - score formula

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

Step2: Calculate z - score for Best Actor

Given $\mu = 45.0$, $\sigma=9.6$, and $x = 54$. Substitute into the formula: $z=\frac{54 - 45.0}{9.6}=\frac{9}{9.6}\approx0.94$.

Step3: Calculate z - score for Best Supporting Actor

Given $\mu = 49.0$, $\sigma = 16$, and $x = 45$. Substitute into the formula: $z=\frac{45 - 49.0}{16}=\frac{- 4}{16}=-0.25$.

Answer:

Best Actor: $z = 0.94$
Best Supporting Actor: $z=-0.25$