1 / 12

Chapter 8 – Normal Probability Distribution

Chapter 8 – Normal Probability Distribution. A probability distribution in which the random variable is continuous is a continuous probability distribution. The normal probability distribution is the most common continuous probability distribution. Nature of the normal distribution.

meagan
Télécharger la présentation

Chapter 8 – Normal Probability Distribution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 8 – Normal Probability Distribution • A probability distribution in which the random variable is continuous is a continuous probability distribution. • The normal probability distribution is the most common continuous probability distribution.

  2. Nature of the normal distribution • Characteristics of normal distribution • Bell-shaped with a single peak • Symmetrical so two halves are mirror images •Look at figure 8-3 on page 164•There are numerous normal distributions that have the same mean, but different standard deviations.•Look at figure 8-4 on page 165.

  3. Importance of the normal distribution. • The normal distribution is very important for two good reasons. • 1. It can be used as an approximation for many other distributions. • 2. Many random variables in the real world follow a normal distribution.

  4. The standard normal distribution • Any normal distribution with a mean and a standard deviation can be converted to a standard normal distribution. The standard normal distribution has a mean of zero and a standard deviation of one. • So the standard normal distribution looks like the one shown below.

  5. Standard Distribution (con’t) • Once converted to the standard normal distribution, the random variable is denoted by Z. The conversion is done by using the following formula: • Z=(X-)/. Formula 8-1 p. 167 • Where X is the original random variable with a mean of  and a standard deviation of .

  6. Standard Distribution (con’t) • Probability of X being greater than 700 is the same as the probability of Z being greater than 2. • P(X>700) = P(Z>2)

  7. Standard Distribution (con’t) • Example Problems 8-1, p. 167 • Z = (700-500) / 100 = 2 300 400 500 600 700 X-Scale -2 -1 0 1 2 Z-Scale

  8. Areas under the normal curve • Areas under the normal curve can be found by using appendix D, p. 478. • Let’s remember a few things1. The area under the normal curve totals 100%. 2. Since the normal curve is symmetrical, 50% of the area is to the right of the mean and the other 50% to the left.

  9. Finding the area • Example problem 8-3, p. 168, • P(Z >1.64)=1- P(Z < 1.64) =1- 0.9495=0.0505 • Example Problem 8-4, page 169 • P(Z > -1.65) = P(Z < 1.65) = 0.9505 • Example Problem 8-5, p. 169-170 • Example Problem 8-6, page 170 • Problem #4, page 173 • Problem #7, page 174 • Problem #10, page 174 • Problem #11, page 174

  10. Applications of Z-score • By now , we know how to use appendix D for finding probabilities. Let’s solve some real-life problems using appendix D. • Example problem 8-10, p. 175 • Example Problem 8-11, p. 176 • Problem#6, p. 180 • Problem #10, p. 181 • Problem #14, p. 181

  11. Sampling Distribution of Mean • If several samples of size n are taken from a population (whose mean is  and standard deviation is ) and their means are computed, these means are normally distributed with a mean of  and a standard deviation of /n.

  12. Central Limit Theorem • Calculation of probabilities for sample _ mean, X: _ X -  Z = --------  / n Formula 8-6, Page 189 •Example Problem 8-16 (Page 190) Problem #5 (Page 191-192), Problem #11 (Page 192-193)

More Related