VCU STAT 210  Lecture19 (78 pages)
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Lecture19
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 Pages:
 78
 School:
 Virginia Commonwealth University
 Course:
 Stat 210  Basic Practice of Statistics
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STAT 210 Lecture 19 Normal Distributions October 9 2017 Practice Problems Pages 162 through 165 Relevant problems VI 1 VI 2 VI 3 VI 5 Recommended problems VI 1 VI 3 VI 5 Additional Reading and Examples Read pages 158 through 160 TOP HAT Distributions When describing a distribution we usually describe four things 1 the center of the distribution 2 the spread or dispersion or variability of the distribution 3 the shape of the distribution 4 any unusual features in the distribution Distributions Two commonly used distributions and the two distributions primarily used in the rest of this course are the normal distributions and the Student s t distributions In this chapter we will discuss and learn the properties associated with these distributions and how to use tables associated with these two distributions Normal Distributions The normal curve is a symmetric bell shaped curve depicted below Data that is described by the normal curve is said to follow a normal distribution A normal distribution is an example of a continuous distribution and hence a normal variable can assume any one of a countless number of possible outcomes Additionally at times one may have a discrete variable and say that the variable has an approximate normal distribution implying that while the discrete variable does not have an exact normal distribution the normal curve is a good approximation for the actual distribution Notation X N m s X is distributed normal with mean m and standard deviation s Notation Example If X is the weight of students and the weights follow a normal distribution with mean 160 pounds and standard deviation 15 pounds then we write X N 160 15 Properties The normal curve is bell shaped Properties The normal curve is bell shaped The peak of the curve is the population mean m Properties The normal curve is bell shaped The peak of the curve is the population mean m The normal curve is symmetric about m m Properties The normal curve is bell shaped The peak of the curve is the population mean m The normal curve is symmetric about m The center and spread are completely specified by specifying the values of the population mean m and the population standard deviation s Properties The normal curve is bell shaped The peak of the curve is the population mean m The normal curve is symmetric about m The center and spread are completely specified by specifying the values of the population mean m and the population standard deviation s The total area under the normal curve is 1 or 100 Properties The normal curve is bell shaped The peak of the curve is the population mean m The normal curve is symmetric about m The center and spread are completely specified by specifying the values of the population mean m and the population standard deviation s The total area under the normal curve is 1 or 100 68 95 99 7 Rule 68 95 99 7 Rule 1 68
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