1 / 16

Econ 3790: Business and Economics Statistics

Econ 3790: Business and Economics Statistics. Instructor: Yogesh Uppal Email: yuppal@ysu.edu. Normal. p ( x ). x. Chapter 6 Continuous Probability Distributions. Normal Probability Distribution. Normal Probability Distribution.

raymondpatterson
Download Presentation

Econ 3790: Business and Economics Statistics

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. Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal Email: yuppal@ysu.edu

  2. Normal p(x) x Chapter 6 Continuous Probability Distributions • Normal Probability Distribution

  3. Normal Probability Distribution • The normal probability distribution is the most important distribution for describing a continuous random variable. • It is widely used in statistical inference.

  4. Normal Probability Distribution • It has been used in a wide variety of applications: Heights of people Scientific measurements

  5. Normal Probability Distribution • It has been used in a wide variety of applications: Test scores • Amounts • of rainfall

  6. Normal f (x) x x1 x2 Normal Distributions • The probability of the random variable assuming a value within some given interval from x1 to x2 is defined to be the area under the curve between x1and x2.

  7. Normal Probability Distribution • Characteristics The distribution is symmetric; its skewness measure is zero. x

  8. Normal Probability Distribution • Characteristics The highest point on the normal curve is at the mean, which is also the median and mode. x Mean = m

  9. Normal Probability Distribution • Characteristics The entire family of normal probability distributions is defined by itsmeanm and its standard deviations . Standard Deviation s x Mean m

  10. Normal Probability Distribution • Characteristics The mean can be any numerical value: negative, zero, or positive. The following shows different normal distributions with different means. x -10 0 20

  11. Normal Probability Distribution • Characteristics The standard deviation determines the width of the curve: larger values result in wider, flatter curves. s = 15 s = 25 x Same Mean

  12. Normal Probability Distribution • Characteristics Probabilities for the normal random variable are given by areas under the curve. The total area under the curve is 1 (.5 to the left of the mean and .5 to the right). .5 .5 x Mean m

  13. Standardizing the Normal Values or the z-scores • Z-scores can be calculated as follows: • We can think of z as a measure of the number of • standard deviations x is from .

  14. Standard Normal Probability Distribution A standard normal distribution is a normal distribution with mean of 0 and variance of 1. If x has a normal distribution with mean (μ) and Variance (σ), then z is said to have a standard normal distribution. s = 1 z 0

  15. Example: Air Quality • I collected this data on the air quality of various cities as measured by particulate matter index (PMI). A PMI of less than 50 is said to represent good air quality. • The data is available on the class website. • Suppose the distribution of PMI is approximately normal.

  16. Example: Air Quality • The mean PMI is 41 and the standard deviation is 20.5. • Suppose I want to find out the probability that air quality is good or what is the probability that PMI is greater than 50.

More Related