# Lecture12 - lecture 12 Continuous Random Variable III 1/27...

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Unformatted text preview: lecture 12, Continuous Random Variable III 1/27 Finding z-Points Normal Ap- proximation More Examples Midterm Related lecture 12, Continuous Random Variable III Outline 1 Finding z-Points 2 Normal Approximation 3 More Examples 4 Midterm Related lecture 12, Continuous Random Variable III 2/27 Finding z-Points Normal Ap- proximation More Examples Midterm Related lecture 12, Continuous Random Variable III Finding z-Points Finding z-Points on a Standard Normal Curve For any 0 < α < 1, z α is the value such that P ( Z ≥ z α ) = α. lecture 12, Continuous Random Variable III 3/27 Finding z-Points Normal Ap- proximation More Examples Midterm Related lecture 12, Continuous Random Variable III Finding z-Points Finding z-Points, ctd • Given an α , how to find z α ? For example, what’s z . 025 ? lecture 12, Continuous Random Variable III 4/27 Finding z-Points Normal Ap- proximation More Examples Midterm Related lecture 12, Continuous Random Variable III Finding z-Points Finding z-Points, ctd Read from the standard normal table that z . 025 ≈ 1 . 96. lecture 12, Continuous Random Variable III 5/27 Finding z-Points Normal Ap- proximation More Examples Midterm Related lecture 12, Continuous Random Variable III Finding z-Points Finding z-Points, ctd • Similarly, z . 05 : • Read from the standard normal table that z . 05 ≈ 1 . 65 • z . 01 ≈ 2 . 33 lecture 12, Continuous Random Variable III 6/27 Finding z-Points Normal Ap- proximation More Examples Midterm Related lecture 12, Continuous Random Variable III Finding z-Points Finding z-Points, ctd • What’s z . 975 ? lecture 12, Continuous Random Variable III 7/27 Finding z-Points Normal Ap- proximation More Examples Midterm Related lecture 12, Continuous Random Variable III Finding z-Points Finding z-Points, ctd • What’s z . 975 ? • Hence z . 975 =- z . 025 ≈ - 1 . 96 lecture 12, Continuous Random Variable III 8/27 Finding z-Points Normal Ap- proximation More Examples Midterm Related lecture 12, Continuous Random Variable III Finding z-Points Finding z-Points, ctd When α > . 5, z α =- z 1- α • z . 95 =- z . 05 ≈ - 1 . 65, z . 99 =- z . 01 ≈ - 2 . 33 lecture 12, Continuous Random Variable III 9/27 Finding z-Points Normal Ap- proximation More Examples Midterm Related lecture 12, Continuous Random Variable III Finding z-Points Example: Inventory Management • A discount store sells packs of 50 DVD’s • Let X be the random variable of weekly demand • Suppose that X is normally distributed with μ = 100 packs, and σ = 10 packs • Q: How many packs should be stocked so that there is only a 5% chance that the store will run short during a week? lecture 12, Continuous Random Variable III 10/27 Finding z-Points Normal Ap- proximation More Examples Midterm Related lecture 12, Continuous Random Variable III Finding z-Points Example: Inventory Management, ctd • Want to find x such that P ( X ≥ x ) = 5 % • Z = ( X- 100 ) / 10 is a standard normal random variable, P ( X ≥...
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## This note was uploaded on 12/28/2010 for the course BUSINESS A ISOM 111 taught by Professor Yingyingli during the Fall '10 term at HKUST.

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Lecture12 - lecture 12 Continuous Random Variable III 1/27...

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