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Unformatted text preview: Chapter 9 : Some Other Points about Normal Distributions A: Prediction intervals Example 1 : The daily sales volume of a small department store has a N(87, 5) distribution where the monetary unit is in $1000. Predict, with 95% probability, tomorrows sales volume. Solution: For any normal distribution N(,) we have from Table B So that a 95% prediction interval for x is With the data that =87 and =5, we have Interpretation : There is a 95% chance that the sales volume will be between 77.2 and 96.8 thousand dollars tomorrow. 96 . 1 ) ( 95 . = x PI ) 96 . 1 96 . 1 ( 95 . + < < = x P ) 8 . 96 , 2 . 77 ( 5 96 . 1 87 ) ( 95 . = = x PI Common prediction intervals B: The SixSigma Criterion Sixsigma is nowadays a rather popular term talked about by managers, quality control engineers and business people. Some authors have written books on it. The basic idea is very simple. Suppose you are a manufacturer. You are concerned about whether the quality of your product can meet customers specifications. 576 . 2 ) ( 960 . 1 ) ( 645 . 1 ) ( 99 . 95 . 90 . = = = x PI x PI x PI Example 2 Manufacturer A is considering signing a contract with customer B to supply him with an electronic device whose resistance is of key concern. Bs requirements are: Resistance = 72.5 2.5 (ohms) i.e. Upper specification limit = USL = 75, Lower specification limit = LSL = 70. A has checked his production conditions and found that his product has a N(72.5, 0.3) Should A accept the deal? Solution : Producers capability is: Resistance=6, i.e. Upper specification limit = UPL = 74.3, Lower specification limit = LPL = 70.7. These production limits are well within Bs specification limits, therefore A can comfortably accept the deal. Note : When the producers sixsigma production limits fall outside the customers specification limits, he should try hard to improve his quality control procedure, particularly in reducing his value. Various people have written books on 6 management. 1. Snee, R.D; & Hoerl, R.W. (2003), Leading Six Sigma, New York Financial Times, PrenticeHall 2. Chowdhury, S. (2002) Design for Sixsigma, New York Financial Times, PrenticeHall C : N(0,1) The Standard Normal Distribution Of all normal distributions N(,), the one with =0 and =1 i.e., the N(0,1)distribution, occupies a special position and has been tabulated (in detail) as in Tables A and B. When we have a general normal distribution X ~ N(,) we often standardize it (or find its S/S ratio) as then by the formulae:  = x z Mean(A+Cx) = A + CMean(x) and s.d.(A+C x)=Cs.d.(x), we have that Mean (z)=0 and S.D....
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This note was uploaded on 04/22/2011 for the course STAT 301 taught by Professor Gabrille during the Spring '11 term at HKU.
 Spring '11
 Gabrille
 Normal Distribution, Probability

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