ch9someotherpointsaboutnormaldistn.studentview

ch9someotherpointsaboutnormaldistn.studentview - Chapter 9...

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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 Six-Sigma Criterion Six-sigma 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 six-sigma 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, Prentice-Hall 2. Chowdhury, S. (2002) Design for Six-sigma, New York Financial Times, Prentice-Hall 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)=|C|s.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.

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ch9someotherpointsaboutnormaldistn.studentview - Chapter 9...

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