the table shows population statistics for the ages of best - actor and best - supporting - actor winners at…

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. compute the z - scores for the actors in the following situation.\nbest actor: $mu = 46.0$, $sigma = 8.8$\nbest supporting actor: $mu = 49.0$, $sigma = 10$\nin a particular year, the best actor was 54 years old and the best supporting actor was 45 years old.\ndetermine the z - scores for each.\nbest actor: $z=square$\nbest supporting actor: $z = square$\n(round to two decimal places as needed.)

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. compute the z - scores for the actors in the following situation.\nbest actor: $mu = 46.0$, $sigma = 8.8$\nbest supporting actor: $mu = 49.0$, $sigma = 10$\nin a particular year, the best actor was 54 years old and the best supporting actor was 45 years old.\ndetermine the z - scores for each.\nbest actor: $z=square$\nbest supporting actor: $z = square$\n(round to two decimal places as needed.)

Answer

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 $\mu_{BA}=46.0$, $\sigma_{BA}=8.8$, and $x_{BA}=54$. $z_{BA}=\frac{54 - 46.0}{8.8}=\frac{8}{8.8}\approx0.91$

Step3: Calculate z - score for Best Supporting Actor

Given $\mu_{BSA}=49.0$, $\sigma_{BSA}=10$, and $x_{BSA}=45$. $z_{BSA}=\frac{45 - 49.0}{10}=\frac{- 4}{10}=-0.40$

Answer:

Best Actor: $0.91$ Best Supporting Actor: $-0.40$