Question

use z scores to compare the given values.
in a recent awards ceremony, the age of the winner for the best actor award was 36 and the age of the winner for the best actress award was 58. for all recipients of best actor, the mean age is 45.4 years and the standard deviation is 7.2 years. for all recipients of best actress, the mean age is 38.7 years and the standard deviation is 11.5 years. (all ages are determined at the time of the awards ceremony.) relative to the award category, who had the more extreme age when winning the award, the winner of best actor or the winner of best actress? explain.
since the z score for the winner of best actor is ( z=square ) and the z score for the winner of best actress is ( z=square ), the winner of ( square ) had the more extreme age.
(round to two decimal places.)

Explanation:

Step1: Calculate the z - score for the Best Actor

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For the Best Actor: \(x = 36\), \(\mu=45.4\), \(\sigma = 7.2\)
\(z_{actor}=\frac{36 - 45.4}{7.2}=\frac{-9.4}{7.2}\approx - 1.31\)

Step2: Calculate the z - score for the Best Actress

For the Best Actress: \(x = 58\), \(\mu = 38.7\), \(\sigma=11.5\)
\(z_{actress}=\frac{58 - 38.7}{11.5}=\frac{19.3}{11.5}\approx1.68\)

The magnitude of the z - score measures the distance from the mean. The magnitude of \(z_{actor}\) is \(|z_{actor}|=1.31\) and the magnitude of \(z_{actress}\) is \(|z_{actress}| = 1.68\)

Answer:

Since the z - score for the winner of Best Actor is \(z=-1.31\) and the z - score for the winner of Best Actress is \(z = 1.68\), the winner of Best Actress had the more extreme age.