Question

30. Total serum cholesterol levels for individuals 65 years of age or older are assumed to follow a normal distribution, with a mean of 182 and a standard deviation of 14.7.

a. What proportion of individuals 65 years of age and older have cholesterol levels of 175 or more?

b. What proportion of individuals 65 years of age and older have cholesterol levels between 150 and 175?

c. If the top 10% of the cholesterol levels are assumed to be abnormally high, what is the upper limit of the normal range?

Answer 1

Solution :

Given that,

mean = = 182

standard deviation = =14.7

A ) P ( x > 175 )

= 1 - P (x < 175 )

= 1 - P ( x -  / ) < ( 175 - 182 / 14.7)

= 1 - P ( z < - 7 / 14.7 )

= 1 - P ( z < - 0.48)

Using z table

= 1 - 0.3156

= 0.6844

Probability = 0.6844

B ) P (150 < x < 175 )

P( 150 - 182 / 14.7) < ( x -  / ) < ( 175 - 182 / 14.7)

P (- 32 / 14.7 < z < - 7 / 14.7 )

P ( - 2.18 < z < - 0.48)

P ( z < - 0.48) - P ( z < - 2.18)

Using z table

= 0.3156 - 0.0146

= 0.3010

Probability = 0.3010

C ) P(Z > z) = 10%

1 - P(Z < z) = 0.10

P(Z < z) = 1 - 0.10 = 0.90

P(Z < 1.282) = 0.90

z = 1.2/

Using z-score formula,

x = z * +

x = 1.28 * 14.7 + 182

= 200.816

The upper limit of the normal range is = 200.8