True or False Statements about Density Curves and Normal Distributions
1. State whether each of the following statements is true or false about Density Curves and Normal Distributions.
1. The total area under any Normal density curve is more than 1.
a. True
b. False
2. The area under the curve between two values represents the probability of the random variable falling within that interval.
a. True
b. False
Final answer:
The total area under any Normal density curve is indeed 1, not more than 1. The area under the curve between two values does represent the probability of the random variable falling within that specified interval, according to the properties of continuous probability distributions.
Explanation: Concerning your questions about Density Curves and Normal Distributions:
False: The total area under any Normal density curve is not more than 1. In fact, it equals 1 according to the probability density function (pdf) properties of continuous probability distributions.
True: The area under the curve between two values does represent the probability of the random variable falling within that interval. For instance, the probability P(a < x < b) is given by the area under the curve from a to b. Normal distributions, characteristically bell-shaped, are vital in many disciplines. The curve of a continuous probability distribution represents probability as area, with outcomes measured and not counted. The entire area under a curve and above the x-axis equates to one. In normal distribution, probability is found for intervals of x-values rather than individual x-values.