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

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

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(x-\mu)/(\sigma)`

P(cholesterol level between 200 and 240 )

`P(200 \leq x \leq 240)\\\\ = P(\displaystyle(200 - 212)/(45.2) \leq z \leq \displaystyle(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.