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 normalcdf function), for \(z = 0.1951\), the left - area \(P(X\leq210)\) (LA) is \(P(Z\leq0.1951)\approx0.5774\) (using a calculator: normalcdf\((-\infty,0.1951)\) with mean \(0\) and standard deviation \(1\)).

Step3: Calculate the right - area (RA)

Since \(P(X>210)=1 - P(X\leq210)\), and \(P(X\leq210)\approx0.5774\)

$$P(X > 210)=1-0.5774 = 0.4226$$

Answer:

\(0.4226\)