4. Boxplot Comparisons Refer to the two STATDISK-generated boxplots shown below

that are drawn on the same scale. One boxplot represents weights of randomly selected men

and the other represents weights of randomly selected women. Which boxplot represents

women? How do you know? Which boxplot depicts weights with more variation?

5. z Score for Helen Mirren's Age As of this writing, the most recent Oscar-winning Best

Actress was Helen Mirren, who was 61 at the time of the award. The Oscar-winning Best Actresses

have a mean age of 35.8 years and a standard deviation of 11.3 years.

a. What is the difference between Helen Mirren's age and the mean age?

b. How many standard deviations is that (the difference found in part (a))?

c. Convert Helen Mirren's age to a z score.

d. If we consider "usual" ages to be those that convert to z scores between and 2, is Helen

Mirren's age usual or unusual?

6. z Score for Philip Seymour Hoffman's Age Philip Seymour Hoffman was 38 years of

age when he won a Best Actor Oscar for his role in Capote. The Oscar-winning Best Actors

have a mean age of 43.8 years and a standard deviation of 8.9 years.

a. What is the difference between Hoffman's age and the mean age?

b. How many standard deviations is that (the difference found in part (a))?

c. Convert Hoffman's age to a z score.

d. If we consider "usual" ages to be those that convert to z scores between and 2, is Hoffman's

age usual or unusual?

7. z Score for Old Faithful Eruptions of the Old Faithful geyser have duration times with a

mean of 245.0 sec and a standard deviation of 36.4 sec (based on Data Set 15 in Appendix B).

One eruption had a duration time of 110 sec.

a. What is the difference between a duration time of 110 sec and the mean?

b. How many standard deviations is that (the difference found in part (a))?

c. Convert the duration time of 110 sec to a z score.

d. If we consider "usual" duration times to be those that convert to z scores between and

2, is a duration time of 110 sec usual or unusual?

8. z Score for World's Tallest Man Bao Xishun is the world's tallest man with a height of

92.95 in. (or 7 ft, 8.95 in.). Men have heights with a mean of 69.6 in. and a standard deviation

of 2.8 in.

a. What is the difference between Bao's height and the mean height of men?

b. How many standard deviations is that (the difference found in part (a))?

c. Convert Bao's height to a z score.

d. Does Bao's height meet the criterion of being unusual by corresponding to a z score that

does not fall between and 2?

9. z Scores for Body Temperatures Human body temperatures have a mean of 98.20F

and a standard deviation of 0.62F (based on Data Set 2 in Appendix B). Convert each given

temperature to a z score and determine whether it is usual or unusual.

a. 101.00F b. 96.90F c. 96.98F

10. z Scores for Heights of Women Soldiers The U.S. Army requires women's heights

to be between 58 in. and 80 in. Women have heights with a mean of 63.6 in. and a standard

deviation of 2.5 in. Find the z score corresponding to the minimum height requirement and

find the z score corresponding to the maximum height requirement. Determine whether the

minimum and maximum heights are unusual.