Chapter 6 Continuous Probability Distributions Case Problem: Specialty Toys 1. Information provided by the forecaster At x = 30‚000‚ [pic] [pic] Normal distribution [pic] [pic] 2. @ 15‚000 [pic] P(stockout) = 1 - .1635 = .8365 @ 18‚000 [pic] P(stockout) = 1 - .3483 = .6517 @ 24‚000 [pic] P(stockout) = 1 - .7823 = .2177 @ 28‚000 [pic]
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F-distribution: A continuous right-skewed statistical distribution also Known as Snedecor’s F distribution or the Fisher - Snedecor distribution ( After R.A. Fisher and George W. Snedecor)(2) which arises in the testing of whether two observed samples have the same variance. (1) Note that three of the most important distributions (namely the normal distribution‚ the t distribution‚ and the chi-square distribution) may be seen as special cases of the F distribution: (3) Example: We want to
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LocatingMiddlemen The search for prospective middlemen should begin with study of the market and determination of criteria for evaluating middlemen servicing that market. The company ’s broad policy guidelines should be followed‚ but expect expediency to override policy at times. The checklist of criteria differs according to the type of middlemen being used and the nature of their relationship with the company. Basically‚ such lists are built around four subject areas: (1) productivity or
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Sean Worang Sustainability 04/19/12 Runa Supply Chain I. Farmers Runa has worked with about 3000 to 4500 Guayusa farmers in the Amazon in regards to the supply and distribution of Guayusa leafs. The result of surveys (done by Runatarpuna) shows that by incorporating above 3000 to 4500 farmers Runa can generate about 16000 pounds/ month and can potentially generate about $17.2 per year projections. II. Runatarpuna Runatarpuna is Runa LLC’s fully owned export subsidiary‚ to manage
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Chapter 13: Chi-Square Applications SHORT ANSWER 1. When samples of size n are drawn from a normal population‚ the chi-square distribution is the sampling distribution of = ____________________‚ where s2 and are the sample and population variances‚ respectively. ANS: PTS: 1 OBJ: Section 13.2 2. Find the chi-square value for each of the right-tail areas below‚ given that the degrees of freedom are 7: A) 0.95 ____________________ B) 0.01 ____________________ C) 0.025 ____________________
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2.3. The Chi-Square Distribution One of the most important special cases of the gamma distribution is the chi-square distribution because the sum of the squares of independent normal random variables with mean zero and standard deviation one has a chi-square distribution. This section collects some basic properties of chi-square random variables‚ all of which are well known; see Hogg and Tanis [6]. A random variable X has a chi-square distribution with n degrees of freedom if it is a gamma
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The Normal and Lognormal Distributions John Norstad j-norstad@northwestern.edu http://www.norstad.org February 2‚ 1999 Updated: November 3‚ 2011 Abstract The basic properties of the normal and lognormal distributions‚ with full proofs. We assume familiarity with elementary probability theory and with college-level calculus. 1 1 DEFINITIONS AND SUMMARY OF THE PROPOSITIONS 1 Definitions and Summary of the Propositions ∞ √ Proposition 1: −∞ 2 2 1 e−(x−µ) /2σ
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Weston Materials‚ Inc.‚ a national manufacturer of unattached garages‚ reports that it takes two construction workers a mean of 32 hours and a standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow the normal distribution. a. Determine the z values for 29 and 34 hours. What percent of the garages take between 32 hours and 34 hours to erect? z(29) = (29-32)/2 = -3/2 z(34) = (34-32)/2 = 1 z(32) = 0 P(32 < x < 34) = P(0< z < 1) = 0.34 b. What percent of the
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X-bar Definition 1 x xi n i 1 Probability and statistics - Karol Flisikowski n Sampling Distribution of x-bar How does x-bar behave? To study the behavior‚ imagine taking many random samples of size n‚ and computing an x-bar for each of the samples. Then we plot this set of x-bars with a histogram. Probability and statistics - Karol Flisikowski Sampling Distribution of x-bar Probability and statistics - Karol Flisikowski Central Limit Theorem The key to the
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AMA470 Midterm exam March 5‚ 2010 Please show full working out in order to obtain full marks. 1. Suppose that: • The number of claims per exposure period follows a Poisson distribution with mean λ = 110. • The size of each claim follows a lognormal distribution with parameters µ and σ 2 = 4. • The number of claims and claim sizes are independent. (a) Give two conditions for full credibility that can be completely determined by the information above. Make sure to define all terms in your definition
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