Question

In a population of adults ages 18 to 65, BMI (body mass index) is normally distributed with a mean of 27 and a standard deviation of 5.

a. What is the BMI score for which half of the population has a lower value?

b. What BMI marks the bottom 25% of the distribution for this population?

c. What BMI marks the bottom 5% of the distribution for this population?

d. What BMI value marks the upper 10% of the distribution for this population?

e. What BMI value marks the upper 30% of the distribution for this population?

Answer 1

a.P(x<z)=0.5

Z=0

$X=z \sigma +\mu=0\times 5+27=27$

b. P(x<z)=0.25

Z=-0.675

$X=z \sigma +\mu=-0.675\times5+27=23.625$

c. P(x<z)=0.05

Z=-1.645

$X=z \sigma +\mu=-1.645\times5+27=18.775$

d. P(x>z)=1-P(x<z)=1-0.1=0.9

Z=1.185

$X=z \sigma +\mu=1.185\times5+27=32.925$

e.P(x>z)=1-P(x<z)=1-0.3=0.7

Z=0.525

$X=z \sigma +\mu=0.525\times5+27=29.625$