PPT-The Normal Distribution

Cal State Northridge 320 Andrew Ainsworth PhD The standard deviation Benefits Uses measure of central tendency ie mean Uses all of the data points Has a special relationship with the normal curve. 1. 4. Continuous Random Variables and Probability Distributions. 4-1 Continuous Random Variables. 4-2 Probability Distributions and Probability Density Functions. 4-3 Cumulative Distribution Functions. History. Abraham de . Moivre. (1733) – consultant to . gamblers. . Pronunciation. .. Pierre Simon . Laplace – mathematician, astronomer, philosopher, determinist.. Carl Friedrich . Gauss – mathematician and astronomer.. http://www-users.york.ac.uk/~pml1/bayes/cartoons/cartoon08.jpg. 1. Comparison of Named Distributions. discrete. continuous. Bernoulli,. Binomial, Geometric, Negative Binomial, Poisson, Hypergeometric, Discrete Uniform. Distributions. Definition. Many sets of data fit what is called a Normal Distribution: EG.  . Examples when the Normal distribution arises. Looking at the national averages for NCEA.. When measuring heights, weights, arm spans, hand spans . Lesson . 2 . Starter: Find . P (. Z<1.63). To do this we begin with a sketch of the normal distribution.. We then mark a line to represent Z=1.63. P(Z<1.63) is the area under the curve to the left of a.. Mat 271E. Yard. Doç. Dr. Tarkan Erdik. Probability Distributions. Uniform and Normal Distributions- Week 7. 1. Probability Distributions. 2. It has been observed that . certain functions . F(x). and . Probability Distribution. Imagine that you rolled a pair of dice. What is the probability of 5-1. ?. To answer such questions, we need to compute the whole population for possible results of rolling two dices. . z. Scores. Chapter 6. The . Bell . Curve is Born (1769). A Modern Normal Curve. Development of a Normal Curve: Sample of 5. Development of a Normal Curve: Sample of 30. Development of a Normal Curve: Sample of 140. @UWE_JT9. @. dave_lush. Scientific . Practice. The Binomial Distribution. This distribution can be seen when the outcomes have discrete values…. eg. rolling dice. Assumptions…. Fixed . number of . . and Exponential Distributions. 5. Introduction. Several specific distributions commonly occur in a variety of business situations:. N. ormal distribution—a continuous distribution . characterized . Binomial Distribution 1. Binomial Distribution 2. Additional Problems on Binomial Distribution. More Visual Representation. Binomial Distribution Tends to Normal for Large n. Binomial Distribution Tends to Normal for p Close to 0.5. It is also known as the Gaussian distribution and the bell curve. .. The general form of its probability density function is-. Normal Distribution in . Statistics. The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. . Dehaish. Outlines. Normal distribution. Standard normal distribution . Find probability when known z score . Find z score from known areas . Conversion to Standard normal distribution.. Sampling distribution of sample mean . ). Let x. i. ~ N(. μ. i. , σ), then the probability density function is defined as. :. Letting: are . independent identical distributed with normal distribution, then the joint distribution of .