L7.1b Continuous Random VariablesCONTINUOUS 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.471-476 #7.7-7.10

Homework:(Review problems p.476-481 #7.16-7.22

Essential Question:

How can you compare probability distributions for discrete and continuous random variables?