Question

please show work

Body mass index (BMI) is computed as the ratio of weight in kilograms to the square of the height in meters.  The distribution of BMI is approximately normal for females aged 30-39. In this group, the mean BMI is 24.5, with a standard deviation of 3.3.

13) What proportion of females aged 30-39 has a BMI of 25 or more?

14) Persons with a BMI of 30 or greater are considered obese.  What proportion of females aged 30-39 is obese?

15) Suppose we classify females aged 30-39 in the top 10% of the BMI distribution as high risk. What is the threshold for classifying a female at high risk? (Hint: use NORMINV)

Answer 1

Solution :

Given that ,

13) P(x 25 ) = 1 - P(x   25 )

= 1 - P[(x - ) / (25 - 24.5) / 3.3]

= 1 -  P(z 0.15)

= 1 - 0.5596

= 0.4404

14) P(x 30 ) = 1 - P(x   30 )

= 1 - P[(x - ) / (30 - 24.5) / 3.3]

= 1 -  P(z 1.67)

= 1 - 0.9525

= 0.0475

15) Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10

= P(Z < z) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.28 ) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 3.3 + 24.5

x = 28.7