Question

The level of cholesterol in the blood of women aged 20 to 55 in a particular country is normally distributed with mean 212 mg/dl and standard deviation 45.2 mg/dl.
The probability that a randomly selected such woman has cholesterol level between 200 and 240 mg/dl is about

Answer 1

Answer:

0.337 is the probability that a randomly selected such woman has cholesterol level between 200 and 240 mg/dl.              

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 212

Standard Deviation, σ = 45.2

We are given that the distribution of level of cholesterol is a bell shaped distribution that is a normal distribution.

Formula:

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

P(cholesterol level between 200 and 240 )

$P(200 \leq x \leq 240)\\\\ = P(\displaystyle\frac{200 - 212}{45.2} \leq z \leq \displaystyle\frac{240-212}{45.2}) \\\\= P(-0.2654 \leq z \leq 0.6194)\\\\= P(z \leq 0.6194) - P(z < -0.2654)\\= 0.732 - 0.395 = 0.337 = 33.7\%$

$P(200 \leq x \leq 240) = 33.7\%$

0.337 is the probability that a randomly selected such woman has cholesterol level between 200 and 240 mg/dl.