The heights of adult men in America are normally distributed, with a mean of 69.5 inches and a standard deviation of 2.62 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.55 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? z = c) Who is relatively taller? O The 6 foot 3 inch American man O The 5 foot 11 inch American woman
The heights of adult men in America are normally distributed, with a mean of 69.5 inches and a standard deviation of 2.62 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.55 inches. a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)? b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)? z = c) Who is relatively taller? O The 6 foot 3 inch American man O The 5 foot 11 inch American woman
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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![**Understanding Z-Scores and Height Distribution**
The heights of adult men in America are normally distributed, with a mean of 69.5 inches and a standard deviation of 2.62 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.55 inches.
**Exercises:**
a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
**Z-score Calculation for Men:**
- Convert height to inches: 6 feet 3 inches = 75 inches.
- Use the formula:
\[
z = \frac{(X - \mu)}{\sigma}
\]
where \( X \) is the height, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
**Z-score Calculation for Women:**
- Convert height to inches: 5 feet 11 inches = 71 inches.
- Use the formula:
\[
z = \frac{(X - \mu)}{\sigma}
\]
where \( X \) is the height, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
c) Who is relatively taller?
- Options:
- The 6 foot 3 inch American man
- The 5 foot 11 inch American woman
**Conclusion:**
Calculate both z-scores to determine who is relatively taller in terms of their respective population distributions.
**Note:** The z-score tells us how many standard deviations an individual's height is from the mean height of the population. The higher the z-score, the taller the individual is relative to their group.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc08ed4ae-4add-4620-b6f7-7adcd6d6aaaa%2Ff8dbe265-15f4-4517-b9fc-57bcfb7bb5b1%2Ft9is32d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Z-Scores and Height Distribution**
The heights of adult men in America are normally distributed, with a mean of 69.5 inches and a standard deviation of 2.62 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.55 inches.
**Exercises:**
a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
**Z-score Calculation for Men:**
- Convert height to inches: 6 feet 3 inches = 75 inches.
- Use the formula:
\[
z = \frac{(X - \mu)}{\sigma}
\]
where \( X \) is the height, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
**Z-score Calculation for Women:**
- Convert height to inches: 5 feet 11 inches = 71 inches.
- Use the formula:
\[
z = \frac{(X - \mu)}{\sigma}
\]
where \( X \) is the height, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
c) Who is relatively taller?
- Options:
- The 6 foot 3 inch American man
- The 5 foot 11 inch American woman
**Conclusion:**
Calculate both z-scores to determine who is relatively taller in terms of their respective population distributions.
**Note:** The z-score tells us how many standard deviations an individual's height is from the mean height of the population. The higher the z-score, the taller the individual is relative to their group.
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