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Sagot :
Using z-scores, we find that:
- The z-score for the female is 0.07.
- The z-score for the male is 0.04.
- Thus, the female is relatively heavier.
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The z-score of a measure X in a data-set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- It measures how many standard deviations X is above or below the mean.
For the female, we have that:
- Mean weight of 156.5 pounds, thus [tex]\mu = 156.5[/tex].
- Standard deviation of 51.2 pounds, thus [tex]\sigma = 51.2[/tex]
- Weighs 160 pounds, thus [tex]X = 160[/tex], and the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 156.5}{51.2}[/tex]
[tex]Z = 0.07[/tex]
The z-score for the female is 0.07.
For the male, we have that:
- Mean weight of 183.4 pounds, thus [tex]\mu = 183.4[/tex].
- Standard deviation of 40 pounds, thus [tex]\sigma = 40[/tex]
- Weighs 185 pounds, thus [tex]X = 185[/tex], and the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{185 - 183.4}{40}[/tex]
[tex]Z = 0.04[/tex]
The z-score for the male is 0.04.
Due to the higher z-score, the female is relatively heavier.
A similar problem is given at https://brainly.com/question/15169808
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