Too much cholesterol in the blood increases the risk of heart disease. The cholesterol levels of young women aged 20 to 34 vary approximately Normally with mean 185 milligrams per deciliter (mg/dl) and standard deviation 39 mg/dl. Cholesterol levels for middle-aged men vary Normally with mean 222 mg/dl and standard deviation 37 mg/dl. Sandy is a young woman with a cholesterol level of 220. Her father has a cholesterol level of 250. Who has relatively higher cholesterol?

### Solution

Let $X$ = The cholesterol levels of young women aged 20 to 34 and $Y$ = Cholesterol levels for middle-aged men.

That is $X\sim N(185,39^2)$ distribution.

The $Z$ score formula is $Z= \dfrac{X-\mu}{\sigma}$.

The cholesterol level of Sandy is 220. Thus the $z$-score for cholesterol level of Sandy is

` $$ \begin{aligned} z_1&=\dfrac{x-\mu}{\sigma}\\ &=\dfrac{220-185}{39}\\ &= 0.897. \end{aligned} $$ `

$Y$ = Cholesterol levels for middle-aged men.

The distribution of $Y$ is $Y\sim N(222, 37^2)$.

The cholesterol level of Sandy's father is 250. Thus the $z$-score for cholesterol level of Sandy's father is

` $$ \begin{aligned} z_2&=\dfrac{x-\mu}{\sigma}\\ &=\dfrac{250-222}{37}\\ &= 0.757. \end{aligned} $$ `

As $z_1> z_2$, Sandy's cholesterol level is relatively higher compared to her father's cholesterol level.

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators