If f (x) is the probability density function for the blood cholesterol level of men over the age of 40, where x is measured in milligrams per deciliter, express as an integral the probability that the cholesterol level of such a man lies between 195 and $250$ .
A) $\int_{40}^{250} f(x) d x$
B) $\int_{0}^{250} f(x) d x$
C) $\int_{195}^{250} f(x) d x$
D) $\int_{40}^{195} f(x) d x$
E) $\int_{250}^{195} f(x) d x$

Question

Quizplus · Accepted Answer

The probability that the cholesterol level of a man lies between 195 and 250 is given by the integral of the probability density function f(x) over the interval [195, 250]. Therefore, the correct integral is: $\int_{195}^{250} f(x) d x$. Choice A is incorrect because it integrates over the interval [40, 250], which includes values outside of the given range of 195 to 250. Choice B is incorrect because it integrates over the entire possible range of cholesterol levels, including values that may not pertain to men over the age of 40. Choice D is incorrect because it integrates over the interval [40, 195], which is not the given range of 195 to 250. Choice E is incorrect because the limits of integration are given in reverse order, which is not valid.

If F (X) Is the Probability Density Function for the Blood