A property of continuous probability distributions is that:
A)Like discrete random variables,the probability distribution can be approximated by a smooth curve.
B)Probabilities for continuous variables can be approximated using discrete random variables.
C)Unlike discrete random variables,probabilities can be found using tables.
D)Unlike discrete random variables,the probability that a continuous random variable equals a specific value is zero;that is,P(X = x)= 0.
E)Unlike discrete random variables,probabilities for continuous random variables can sum to a value greater than 1.

Question

Quizplus · Accepted Answer

This is the property of continuous probability distributions that distinguishes them from discrete random variables. Since a continuous random variable can take on an infinite number of values within an interval, the probability that it equals a specific value is zero. This is because the area under the probability density function between two neighboring points on the interval is what gives the probability of the variable being in that range, and the width of a single point on the interval is zero.

A Property of Continuous Probability Distributions Is That