Algebra - Find Z-scores

Algebra
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In a random sample of adults aged 20-29, the middle 95% of the men are between 168 and 191 cm tall, and the middle 95% of the women are between 155 and 174 cm tall. The heights of each sex follow a normal distribution. Robert and Amanda are both 25 years old, and Robert is 12.7 cm taller than Amanda. Find their respective z-scores.

May 20th, 2015

roberts has a 0.95 significance

the mean of men's height is (191+168)/2= 179.5

mean for women =(155+174)/2= 164.5

the z-test for Robert p(z)=1-0.95

1-p(z)

but Z(0.95)=1.645

the z score of Robert is 1-1.645=0.645

for Amanda (x-12.7)+16.45=1.645

hence amandas zscore is z(-2.26)= 0.01222

May 20th, 2015

Thank you for posting the solution. I do have a question: The z-score of Robert is (1 - 1.645), which should have a negative sign -0.645. But you came up with his z-score as a positive number. Why?

 

May 20th, 2015

the negative is used to show the side of the Z value in the distribution curve. in calculations, the negative sign is not applicable

May 20th, 2015

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