Question

Cholesterol levels for a group of men aged 30-39 follow an approximately normal distribution with mean 193.15 milligrams per deciliter (mg/dl). Medical guidelines state that men with cholesterol levels above 240 mg/dl are considered to have high cholesterol and about 9.1% of men fall into this category. 1. What is the Z-score that corresponds to the top 9.1% (or the 90.9-th percentile) of the standard normal distribution?

Answer 1

for top 9.1% z- score is 1.33

Explanation:

given data:

x = 240 mg/dl

`mean\ \mu = 193.15`

1) from standard table for z

`P(Z>\tau) = 9.1\%`

`1 - P(Z< \tau) = 0.091`

`P(Z< \tau) = 1 - 0.091`

`P(Z< \tau) = 0.909`

P(Z< 1.33) = 0.091

z = 1.33

therefore for top 9.1% z- score is 1.33