Question

the blood cholesterol levels for u.s. adults are normally distributed, with \\( \mu = 202 \\) and \\( \sigma = 41 \\) (units in milligrams per deciliter). find \\( p(x>210) \\).
enter your answer as an area under the curve with 4 decimal places.
\\( p(x>210)= \\)________
(this problem is just like ch 6.1 so you are calculating a regular z - score and looking up the la, then finding \\( ra = 1 - la \\).)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\). Given \(x = 210\), \(\mu=202\), and \(\sigma = 41\).

$$ z=\frac{210 - 202}{41}=\frac{8}{41}\approx0.1951 $$

Step2: Find the left - area (LA)

Using the standard normal distribution table or a calculator with a normal distribution function (\(\text{normalcdf}(-\infty,z)\)), for \(z = 0.1951\), the left - area \(LA=\Phi(0.1951)\approx0.5774\) (using a calculator: \(\text{normalcdf}(-1000,0.1951)\) where \(- 1000\) approximates \(-\infty\) in the context of the standard normal distribution).

Step3: Calculate the right - area (RA)

Since \(RA = 1 - LA\), then \(RA=1 - 0.5774=0.4226\)

Answer:

\(P(X>210)=0.4226\)