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 245 .
A) $\int _ { 40 } ^ { 195 } f ( x ) d x$
B) $\int _ { 245 } ^ { 195 } f ( x ) d x$
C) $\int _ { 40 } ^ { 245 } f ( x ) d x$
D) $\int _ { 195 } ^ { 245 } f ( x ) d x$
E) $\int _ { 0 } ^ { 245 } f ( x ) d x$

Question

Quizplus · Accepted Answer

We want to find the probability that the cholesterol level is between 195 and 245, which is the same as finding the area under the density curve between those two values. This can be expressed as the integral from 195 to 245 of the density function: $\int_{195}^{245} f(x) dx$. Thus, the correct answer is (D).

If f(x)f ( x )f(x) Is the Probability Density Function for the Blood Cholesterol Level

If $f ( x )$ Is the Probability Density Function for the Blood Cholesterol Level