Question

The distribution of cholesterol levels in teenage boys is approximately normal with and (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 225.

Answer 1

Answer:

0.033 is the probability that a teenage boy has a cholesterol level greater than 225.

Step-by-step explanation:

The following information is missing in the question:

Mean, μ = 170

Standard Deviation, σ = 30

Using the given information, we may solve the question as:

We are given that the distribution of distribution of cholesterol levels in teenage boys is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P( cholesterol level greater than 225)

P(x > 225)

$P( x > 225) = P( z > \displaystyle\frac{225 - 170}{30}) = P(z > 1.833)$

$= 1 - P(z \leq 1.833)$

Calculation the value from standard normal z table, we have,  

$P(x > 225) = 1 - 0.967= 0.033 = 3.3\%$

0.033 is the probability that a teenage boy has a cholesterol level greater than 225.