n a recent awards ceremony, the age of the winner for best actor was 35 and the age of the winner for best actress was 48. For all best actors, the mean age is 48.7 years and the standard deviation is 8.9 years. For all best actresses, the mean age is 34.7 years and the standard deviation is 11.7 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who had the more extreme age when winning the award, the actor or the actress? Explain.

The best actor's age is farther from the mean, so he has the more extreme age when winning the award

Step-by-step explanation:

Z-score:

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

Whichever z-score's has the highest absolute value, that is, is farther from the mean, has the most extreme age.

Best actor:

Age of 35, so .

For all best actors, the mean age is 48.7 years and the standard deviation is 8.9 years, so

Best actrees:

Age of 48, so

For all best actresses, the mean age is 34.7 years and the standard deviation is 11.7 years, so

The best actor's age is farther from the mean, so he has the more extreme age when winning the award

step-by-step explanation: