Body mass index (BMI) for men age 60 is normally distributed with mean of 29 and
ID: 3173345 • Letter: B
Question
Body mass index (BMI) for men age 60 is normally distributed with mean of 29 and standard deviation of 6? What is the probability that a male has a BMI less than 29? What is the probability that a male has a BMI less than 35? What is the probability that a male has a BMI less than 30? What is the probability that a man has a normal BMI (between 18 5 and 24 9? BMI in men follows a normal distribution with m=29, s=6. BMI in women follows a normal distribution with m=28. S=7. What is the 90^th percentile of BMI for men? What is the 90^th percentile of BMI for women?Explanation / Answer
from normal distribution
zscore =(X-mean)/std deviation
hence a) P(X<29)=P(Z<(29-29)/6)=P(Z<0)=0.5
b)P(X<35)=P(Z<!)=0.8413
c)P(X<30)=P(Z<0.1667)=0.5662
d)P(18.5<X<24.9)=P(-1.75<Z<-0.6833)=0.2472-0.0401=0.2071
5)for 92 percentile ; z score =1.28
hence corresponding socre for men =mean +z*std deviation =29+6*1.28=36.69
and corresponding socre for women =mean +z*std deviation =28+7*1.28=36.97