Your body mass index (BMI) is your weight in kilograms divided by the square of

Question

Your body mass index (BMI) is your weight in kilograms divided by the square of your height in meters. High BMI is a common - and VERY controversial - indicator of being overweight or obese. A study for the USA National Center for Health Statistics found that the BMI of USA women, aged 20-29, is normally distributed with a mean of 26.5 and standard deviation of 6.4. People with a BMI of under 18.5 are classified as "underweight". By this classification, what proportion of women, aged 20-29, in the USA are underweight If a random sample of 9 women are selected from this population is selected, what is the probability that the sample mean BMI will be below 24.9

Explanation / Answer

a.For X=18.5, z=(x-mu)/sigma

=(18.5-26.5)/6.4

=-1.25

Now, find, P(X<18.5)=P(z<-1.25)=0.1056

b.Using Centrla limit theorem the sampling distribution of sample mean is also normal with mean mu=26.5 and standard deviation=sigma/root over n=6.4/3=2.13

For X=24.9, z=(24.9-26.5)/6.4=-0.25

P(X<24.9)=P(z<-0.25)=0.4013

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