Answer:
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 ![\mu = 48.7, \sigma = 8.9](https://tex.z-dn.net/?f=%5Cmu%20%3D%2048.7%2C%20%5Csigma%20%3D%208.9)
![Z = -1.54](https://tex.z-dn.net/?f=Z%20%3D%20-1.54)
Best actrees:
Age of 48, so ![X = 48](https://tex.z-dn.net/?f=X%20%3D%2048)
For all best actresses, the mean age is 34.7 years and the standard deviation is 11.7 years, so ![\mu = 34.7, \sigma = 11.7](https://tex.z-dn.net/?f=%5Cmu%20%3D%2034.7%2C%20%5Csigma%20%3D%2011.7)
![Z = 1.14](https://tex.z-dn.net/?f=Z%20%3D%201.14)
The best actor's age is farther from the mean, so he has the more extreme age when winning the award