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

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.\nbest actor\tbest supporting actor\nμ = 45.0\tμ = 49.0\nsigma = 9.6\tsigma = 16\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=\nbest supporting actor: z=\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. compare the z - scores for the actors in the following situation.\nbest actor\tbest supporting actor\nμ = 45.0\tμ = 49.0\nsigma = 9.6\tsigma = 16\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=\nbest supporting actor: z=\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 $\mu = 45.0$, $\sigma=9.6$, 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: $z=-0.25$