Assume heights and weights are normally distributed with the given means and standard deviations from the table below.

Strata Mean Standard Deviation Mean Standard Deviation
Height Height Weight Weight
(inches) (inches) (pounds) (pounds)
U.S. Men 69.3 2.8 191 28
U.S. Women 64.4 2.8 141 32
NFL Quarterbacks 76.5 1.8 245 25
Top Female Models 70.0 2.2 115 18
Gisele Bundchen is a top female model. She is 71 inches tall and weighs 115 pounds. Round your z-scores to 2 decimal places.
(a) With respect to all U.S. women, the z-score for her height is WebAssign will check your answer for the correct number of significant figures.-1.48
Incorrect: Your answer is incorrect.
.

(b) With respect to all U.S. women, the z-score for her weight is WebAssign will check your answer for the correct number of significant figures. .

(c) With respect to all U.S. women, would her height be considered unusual?
Yes
No
Correct: Your answer is correct.

(d) With respect to all U.S. women, would her weight be considered unusual?
Yes
No
Correct: Your answer is correct.

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a and b. Z = (score-mean)/SD

What were your answers to c and d?

To determine the z-score for Gisele Bundchen's height and weight with respect to all U.S. women, we can use the formula:

z = (x - μ) / σ

where:
- z is the z-score
- x is the value we are comparing (in this case, Gisele Bundchen's height and weight)
- μ is the mean of the distribution
- σ is the standard deviation of the distribution

(a) For Gisele Bundchen's height:

z = (71 - 64.4) / 2.8
z ≈ -1.48

Round the z-score to 2 decimal places: -1.48

(b) For Gisele Bundchen's weight:

z = (115 - 141) / 32
z ≈ -0.813

Round the z-score to 2 decimal places: -0.81

(c) To determine if Gisele Bundchen's height is considered unusual with respect to all U.S. women, we look at the z-score. A z-score greater than 2 or less than -2 is generally considered unusual. In this case, -1.48 is within the range of -2 to 2, so her height would not be considered unusual.

Answer: No

(d) To determine if Gisele Bundchen's weight is considered unusual with respect to all U.S. women, we look at the z-score. Again, a z-score greater than 2 or less than -2 is generally considered unusual. In this case, -0.81 is within the range of -2 to 2, so her weight would not be considered unusual.

Answer: No