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# Supplement_4 - NORMAL DISTRIBUTION THE NORMAL DISTRIBUTION...

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≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ NORMAL DISTRIBUTION ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ THE NORMAL DISTRIBUTION Documents prepared for use in course C22.0103.001, New York University, Stern School of Business Use of normal table, standardizing forms page 3 This illustrates the process of obtaining normal probabilities from tables. The standard normal random variable (mean = 0, standard deviation = 1) is noted here, along with adjustment for normal random variables in which the mean and standard deviation are general. Inverse use of the table is also discussed. Additional normal distribution examples page 8 This includes also a very brief introduction to the notion of control charts. Normal distributions used with sample averages and totals page 12 This illustrates uses of the Central Limit theorem. Also discussed is the notion of selecting, in advance, a sample size n to achieve a desired precision in the answer. How can I tell if my data are normally distributed? page 19 We are very eager to assume that samples come from normal populations. Here is a display device that helps to decide whether this assumption is reasonable. Central limit theorem page 23 The approximate normal distribution for sample averages is the subject of the Central Limit theorem. This is a heavily-used statistical result, and there are many nuances to its application. 1

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≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ NORMAL DISTRIBUTION ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ Normal approximation for finding binomial probabilities page 29 The normal distribution can be used for finding very difficult binomial probabilities. Another layout for the normal table page 31 The table listed here gives probabilities of the form P[ Z z ] with values of z from -4.09 to +4.09 in steps of 0.01. The random walk model for stock prices page 34 This is a discussion of the commonly-used random walk model. It’s given here is its simple form and also in its more useful log-normal form. revised by Avi Giloni Gary Simon, 2003 Cover photo: Poison ivy plants, Cedar Beach, Mount Sinai, New York 2
ÚÚÚÚÚÚÚÚ USE OF NORMAL TABLE ÚÚÚÚÚÚÚÚ The standard normal distribution refers to the case with mean µ = 0 and standard deviation σ = 1. This is precisely the case covered by the tables of the normal distribution. It is common to use the symbol Z to represent any random variable which follows a normal distribution with µ = 0 and σ = 1. The normal distribution is often described in terms of its variance σ 2 . Clearly σ is found as the square root of σ 2 . If X is a normal random variable with general mean µ (not necessarily 0) and standard deviation σ (not necessarily 1), then it can be converted to standard normal by way of Z = X −µ σ or equivalently X = µ + σ Z The act of subtracting the mean and then dividing by a standard deviation is called “standardizing,” and it enables you to use the normal table.

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Supplement_4 - NORMAL DISTRIBUTION THE NORMAL DISTRIBUTION...

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