Respuesta :
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 [tex]X = 35[/tex].
For all best​ actors, the mean age is 48.7 years and the standard deviation is 8.9 years, so [tex]\mu = 48.7, \sigma = 8.9[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 48.7}{8.9}[/tex]
[tex]Z = -1.54[/tex]
Best actrees:
Age of 48, so [tex]X = 48[/tex]
For all best​ actresses, the mean age is 34.7 years and the standard deviation is 11.7 years, so [tex]\mu = 34.7, \sigma = 11.7[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48 - 34.7}{11.7}[/tex]
[tex]Z = 1.14[/tex]
The best actor's age is farther from the mean, so he has the more extreme age when winning the​ award
