Question

Find the standard deviation of the distribution in the following situations. (Round your answers to two decimal places.) (a) MENSA is an organization whose members 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.

Answer 1

Answer:

a) 15.579

b) 39.019

Step-by-step explanation:

a) For the top 2% the z-value from the z table

z = 2.054

thus,

z = $\frac{\textup{X-Mean}}{\sigma}$

here

X = 132

Mean = 100

thus,

2.054 = $\frac{\textup{132-100}}{\sigma}$

or

σ = 15.579

b) Using tables, we get for Z = 0.89 the value of 0.8133 and for Z= 0.90 the value of 0.8159

By interpolation, values for 0.815 and we get Z=0.897

thus,

z = $\frac{\textup{X-Mean}}{\sigma}$

here

X = 220

Mean = 185

thus,

0.897 = $\frac{\textup{220-185}}{\sigma}$

or

σ = 39.019