When you have completed this chapter, you will be able to: Explain how probabilities are assigned to a continuous random variable, explain the characteristics of a normal probability distribution, define and calculate z value corresponding to any observation on a normal distribution, determine the probability a random observation is in a given interval on a normal distribution using the standard normal distribution, use the normal probability distribution to approximate the binomial probability distribution.
7 1 THE Normal PROBABILITY DISTRIBUTION Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 7 2 When you have completed this chapter, you will be able to: Explain how probabilities are assigned to a continuous random variable Explain the characteristics of a normal probability distribution Define and calculate z value corresponding to any observation on a normal distribution Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 7 3 Determine the probability a random observation is in a given interval on a normal distribution using the standard normal distribution. Use the normal probability distribution to approximate the binomial probability distribution Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 7 4 Continuous Random Variable Continuous Random Variable …the set of all the values in any interval is ….we will now study the class of uncountable or infinite! ….we will now study the class of continuous probability distributions continuous probability distributions Recall… Recall… Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Variables 7 5 Quantitative … can be classified as either Discrete or Continuous Numerical Observations Continuous Continuous Characteristics Characteristics … can assume any any value value … can assume within a specified within a specified range! range! e.g. Pressure in a tire Weight of a pork chop Height of students in a class Also Recall that… Also Recall that… Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Continuous Random Variable 7 6 Continuous Random Variable …the Total sum of probabilities …the Total sum of probabilities should always be 1! should always be 1! When dealing with a When dealing with a Continuous Random Variable Continuous Random Variable we assume that we assume that the probability that the variable the probability that the variable will take on any particular will take on any particular value is 0! is 0! value Instead, Instead, Probabilities are assigned to intervals of values! Probabilities are assigned to intervals of values! Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Continuous Probability 7 7 Distributions Range of Values Range of Values f(x) P(a