The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. Find the probability that a
Teenage boy has a cholesterol level greater than 200.
A)0.1587
B)0.8413
C)0.3419
D)0.2138

Question

Quizplus · Accepted Answer

To find the probability that a teenage boy has a cholesterol level greater than 200, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (200), $\mu$ is the mean (170), and $\sigma$ is the standard deviation (30). Plugging in the values, we get $Z = \frac{200 - 170}{30} = 1$. Looking up the Z-score of 1 in a standard normal distribution table or using a calculator, we find that the area to the left of Z=1 is approximately 0.8413. Since we want the area to the right (the probability of being greater than 200), we subtract this from 1, resulting in $1 - 0.8413 = 0.1587$.

The Distribution of Cholesterol Levels in Teenage Boys Is Approximately μ\muμ

The Distribution of Cholesterol Levels in Teenage Boys Is Approximately $\mu$