A continuous random variable is a random variable that can take on all values in an interval.
A density curve is an idealized representation of a distribution in which the area under the curve is defined as 1, or in terms of percentages, a probability of 100%.
discrete random variables
Discrete random variables represent the number of distinct values that can be counted of an event.
The empirical rule states that for data that is normally distributed, approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data will fall within three standard deviations of the mean.
An inflection point is a point in the domain where concavity changes from positive to negative or negative to positive.
The normal curve is the curve that defines the probability density graph for a normally distributed variable.
normal density curve
A normal density curve is a density curve for a normal distribution.
probability density function
A function is called a probability density function if for all , the area under the graph of over all real numbers is exactly 1, and the probability that is in the interval is .
The square root of the variance is the standard deviation. Standard deviation is one way to measure the spread of a set of data.
A measure of the spread of the data set equal to the mean of the squared variations of each data value from the mean of the data set.
The z -score of a value is the number of standard deviations between the value and the mean of the set.
A z-score table associates the various common z-scores between 0 and 3.99 with the decimal probability of being less than or equal to that z-score.
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This Concept expands upon the previous by discussing further the normal distribution and the probabilities associated with it by looking at the normal density curve.