Convert Ken's chest, waist, and hips measurements to z-scores. Which of these measures appears to be the most different from kens reference group(human males)? Justify with an appropriate statistical argument.

Ken's chest=75.0,waist=56.5,hips=72.0
Human x-bar chest is 91.2,waist is 80.9,hips are 93.7 .
Human S chest is 4.8, waist is 9.8, hips is 6.8.
THANKS FOR ANY HELP NEED IT ALOT!!!!

Z = (score-mean)/SD

Which Z scores are the greatest?

55666

the z scores for ken's chest, waist and hips are -3.4, -2.5 and -3.2,

To convert Ken's measurements to z-scores, we'll use the formula:

Z = (X - μ) / σ

Where:
- Z is the z-score
- X is Ken's measurement
- μ is the mean of the reference group
- σ is the standard deviation of the reference group

Let's calculate the z-scores for each measurement:

For the chest measurement:
Z_chest = (75.0 - 91.2) / 4.8
Z_chest ≈ -3.36

For the waist measurement:
Z_waist = (56.5 - 80.9) / 9.8
Z_waist ≈ -2.49

For the hips measurement:
Z_hips = (72.0 - 93.7) / 6.8
Z_hips ≈ -3.19

Now, we will compare the absolute values of these z-scores to determine which measure appears to be the most different from Ken's reference group (human males).

The absolute values are:
|Z_chest| ≈ 3.36
|Z_waist| ≈ 2.49
|Z_hips| ≈ 3.19

Since the absolute value of Z_waist is the smallest among the three, it appears to be the least different from Ken's reference group (human males). This means that Ken's waist measurement aligns relatively closely with the average waist measurement of human males.

On the other hand, the absolute values of Z_chest and Z_hips are larger. This suggests that Ken's chest and hip measurements are more different from the reference group, indicating that they deviate more from the average measurements of human males.

Please note that this conclusion is based on the assumption that the distribution of chest, waist, and hip measurements follows a normal distribution, and that the reference group's mean and standard deviation are appropriate for comparison.