# Shared Flashcard Set

## Details

S7.1 - Properties of the Normal Distribution
Properties of the Normal Distribution
19
Mathematics
11/07/2013

Term
 Uniform probability distribution
Definition
 Distribution where the intervals of random variable X have an equal probabilitiy of occurring
Term
 Probability density function, (pdf)
Definition
 An equation used to compute probabilities of continuous random variables
Term
 2 properties of pdf
Definition
 1. The total area under the graph of the equation over all possible values of the random variable must equal 12. The graph of the equation must lie on or above the horizontal axis for all possible values of the random variable
Term
 The area under the graph of a density function represents
Definition
 The probability of observing a value of the random variable in that interval
Term
 Normally distributed
Definition
 A continuous random variable that has a normal probability distribution
Term
 Inflection points
Definition
 Points on the normal curve where the curvature of the graph changes
Term
 2 inflection points, x =
Definition
 1. mew - sigma2. mew + sigma
Term
 1. Properties of the normal density curve
Definition
 It is symmetric about its mean, mew
Term
 2. Properties of the normal density curve
Definition
 Mean = median = mode, and there is a single peak and the highest point occurs at x = mew
Term
 3. Properties of the normal density curve
Definition
 I has inflection points mew - sigma and mew + sigma
Term
 4. Properties of the normal density curve
Definition
 The area under the curve is 1
Term
 5. Properties of the normal density curve
Definition
 The area under the curve to the right of mew equals the area under the curve to the left of mew
Term
 6. Properties of the normal density curve
Definition
 A x increases/decreases without bound, the graph approaches but never reaches the horizontal axis
Term
 7. Properties of the normal density curve
Definition
 Empirical rule
Term
 1. Empirical rule
Definition
 Approximately 68% of the area under the normal curve is between x = mew - sigma and x = mew + sigma
Term
 2. Empirical rule
Definition
 Approximately 95% of the area under the normal curve is between x = mew - 2sigma and x = mew + 2sigma
Term
 3. Empirical rule
Definition
 Approximately 99.7% of the area under the normal curve is between x = mew - 3sigma and x = mew + 3sigma
Term
 The area under the normal curve for any interval of values of the random variable X represents either
Definition
 1. The proportion of the population with the characteristic described by the inverval of values2. The probability that a randomly selected individual from the population will have the characteristic described by the interval of values
Term