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In the set of all best actors, the mean age is 44.1 years, and the standard deviation of the ages is 8.9 years.

The age of the actorEddie Redmayne is 33.

For all best actresses, the mean age is 36.2 years, and the standard deviation of the ages is 11.5 years.

The age of the actress Julianne Moore is 54.

Define M as the age of actors and F as the age of actresses.

Then,

$$\begin{gathered} {\stackrel{炉}{x}}_M=44.1 \\ {s}_M=8.9 \\ m=33 \end{gathered}$$

$$\begin{gathered} {\stackrel{炉}{x}}_F=36.2 \\ {s}_F=11.5 \\ f=54 \end{gathered}$$

A z-score is a standard value is computed to know how far and in what direction from the mean is the raw value.

It has the following expression:

$Z=\frac{x-\stackrel{炉}{x}}{s}$

When the absolute z-score is large (in absolute terms), it suggests a larger difference from the mean value in terms of standard deviations.

The z-score for the actor is as follows:

$$\begin{gathered} Z=\frac{m-{\stackrel{炉}{x}}_M}{s_M} \\ =\frac{33-44.1}{8.9} \\ =-1.25 \end{gathered}$$

The z-score for the actress is as follows:

$$\begin{gathered} Z=\frac{f-{\stackrel{炉}{x}}_F}{s_F} \\ =\frac{54-36.2}{11.5} \\ =1.55 \end{gathered}$$

Therefore, -1.25is thez-score for Eddie Redmayne鈥檚 age, and 1.55 is theZ-score for Julianne Moore鈥檚 age.

Julianne鈥檚 age equal to 54 years is 1.55 standard deviations above the mean, and Eddie鈥檚 age equal to 33 years is 1.25 standard deviations below the mean.

The z-score of 1.55 is farther from the mean as compared to 1.25. Thus,Julianne Moore鈥檚 age is more extreme than Eddie Redmayne鈥檚 age.