Find the SD Find the standard deviation of the distribution

Find the SD. Find the standard deviation of the distribution in the following situations.

a) MENSA is organization whose member have IQs in the top 2% of the population. IQs are normally distributed with mean 100, and the minimum IQ score required for admission to MENSA is 132.

(b) Cholesterol levels for women aged 20 to 34 follow an approximately normal distribution with mean 185 milligrams per deciliter (mg/dl). Women with cholesterol levels above 220 mg/dl are considered to have high cholesterol and about 18.5% of women fall into this category.

Solution

Find the SD. Find the standard deviation of the distribution in the following situations.

From standard normal table z value for top 2% =2.054

132 = 100+2.054*sd

Sd =(132-100)/2.054=15.58

(b) Cholesterol levels for women aged 20 to 34 follow an approximately normal distribution with mean 185 milligrams per deciliter (mg/dl). Women with cholesterol levels above 220 mg/dl are considered to have high cholesterol and about 18.5% of women fall into this category.

From standard normal table z value for top 18.5% =0.896

220 = 185+0.896*sd

Sd= (220-185)/0.896 =39.06