L7.1b Continuous Random Variables CONTINUOUS RANDOM VARIABLES NORMAL DISTRIBUTIONS AD PROBABILITY DISTRIBUTIONS

Standard:MCC9-12.S.MD.1  S-MD.1. (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

Learning Target  Students will define a continuous random variable and a probability distribution for a continuous random variable.

Vocabulary:  A continuous random variable X takes all the values in an interval of numbers.  The probability distribution of X is described by a density curve.  A uniform distribution refers to a probability distribution for which all of the values that a random variable can take on occur with equal probability.

Notes:  All continuous probability distributions assign probability 0 to each individual outcome. Unlike discrete random variables, in continuous random variables, only intervals of values have positive probability. (the probability of any interval is the same as the length, a single point has no length, therefore its probability would be 0).  Normal distributions are probability distributions.  The total area under a density curve is always 1, corresponding to the total probability of 1.

Uniform Distributions  The probability is equal to the area below the curve, length of the interval times the height of the distribution.  Example: a uniform distribution with a height of 1 over the interval of 0 to 1, the area, and thus the probability, can be calculated by multiplying the length of the interval by 1.  P(X≤0.5) = 1x0.5 =.5 or 50%  P(0.3 ≤ X ≤ 0.7) = 1x 0.4 = 0.4 or 40%

The Normal Distribution

Work Session:  The Practice of Statistics text p #  Homework:(Review problems p #

Essential Question:  How can you compare probability distributions for discrete and continuous random variables?