Question

Obesity is identified as the primary cause of chronic illness in young Australian women. Based on historical data (not the sample data in women20.sav), the age of obese young Australian women is approximately normally distributed with a mean of 28 years and a standard deviation of 1.5 years.

(a) Identify the variable of interest and the unit of measurement of the variable that can be used to estimate the probabilities of the ages of obese young Australian women.

(b) Based on the above normal distribution, what proportion of obese young Australian women are aged 30 years or more?

(c) Based on the above normal distribution, above what age are the oldest 15% of obese young Australian women?

Answer 1

Solution:

Given: the age of obese young Australian women is approximately normally distributed with a mean of 28 years and a standard deviation of 1.5 years.

Mean = years

Standard deviation = years

Part a) Identify the variable of interest and the unit of measurement of the variable that can be used to estimate the probabilities of the ages of obese young Australian women.

The variable of interest = The age of obese young Australian women

The unit of measurement of the variable = Years.

Part b) Based on the above normal distribution, what proportion of obese young Australian women are aged 30 years or more?

Find z score for x = 30

Thus we get:

Look in z table for z = 1.3 and 0.03 and find corresponding area.

P( Z < 1.33 ) = 0.9082

Thus

Part c) Based on the above normal distribution, above what age are the oldest 15% of obese young Australian women?

That is find x value such that:

P( X > x) =15%

P( X > x) =0.15

Thus find z value such that:

P(Z > z )= 0.15

that is:

P(Z < z ) = 1 - P(Z > z )

P(Z < z ) = 1 - 0.15

P(Z < z ) = 0.85

Look in z  table for Area = 0.8500 or its closest area and find corresponding z value.

Area 0.8508 is closest to 0.8500 and it corresponds to 1.0 and 0.04

that is  z = 1.04

Now use following formula to find x value:

Thus age above 29.56 years are the oldest 15% of obese young Australian women.