Comparing Values. In Exercises 13–16, use z scores to compare the given values.

Oscars As of this writing, Sandra Bullock was the last woman to win an Oscar for Best Actress and Jeff Bridges was the last man to win for Best Actor. At the time of the awards ceremony, Sandra Bullock was 45 years of age and Jeff Bridges was 60 years of age. Based on Data Set 11 in Appendix B, the Best Actresses have a mean age of 35.9 years and a standard deviation of 11.1 years. The Best Actors have a mean age of 44.1 years and a standard deviation of 9.0 years. (All ages are determined at the time of the awards ceremony.) Relative to their genders, who was younger when winning the Oscar: Sandra Bullock or Jeff Bridges? Explain

Answer :

Step 1 of 1 :

Given Sandra Bullock was 45 years of age.

x = 45

The Best Actresses have a mean age of 35.9 years and a standard deviation of 11.1 years.

Here mean and standard deviation

we have to find the Sandra Bullock z-score.

The formula of the z-score is

z =

Substitute x , and values.

z =

z =

z = 0.8198

Therefore Sandra Bullock z-score is 0.82.

Given Jeff Bridges was 60 years of age.

x = 60

The Best Actors have a mean age of 44.1 years and a standard deviation of 9.0 years.

Here mean and standard deviation

we have to find the Jeff Bridges z-score.

The formula of the z-score is

z =

Substitute x , and values.

z =

z =

z = 1.766

Therefore Sandra Bullock z-score is 1.77.

Sandra Bullock was relatively younger than Jeff Bridges,because she has a smaller z-score.