ch5-6_notes

ch5-6_notes - x MGMT 305 Business Statistics f(x)...

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μ x x f f ( ( x x ) ) Π29 ⌠Φ 0 υ { ÷ ♠ Ν ζ Ξ ƒ Α + ξ MGMT 305 Business Statistics Probability Distributions Outline: §5.4: Binomial Probability Distribution §6.2: Normal Probability Distribution Binomial Probability Distribution: Properties of a Binomial Experiment: 1. The experiment consists of a sequence of n identical trials. 2. Two outcomes, success and failure , are possible on each trial. 3. The probability of a success, denoted by p , does not change from trial to trial. 4. The trials are independent. Binomial Probability Function: where: f ( x ) = the probability of x successes in n trials n = the number of trials p = the probability of success on any one trial 1
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Example 1: Evans Electronics Evans is concerned about a low retention rate for employees. On the basis of past experience, management has seen a turnover of 10% of the hourly employees annually. Thus, for any hourly employees chosen at random, management estimates a probability of 0.1 that the person will not be with the company next year. Choosing 3 hourly employees at random, what is the probability that 1 of them will leave the company this year? Method I: Using the Binomial Probability Function 2
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Method II: Using the Binomial Tables 3
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Binomial Probability Distribution: Expected Value E ( x ) = μ = np Variance Var( x ) = σ 2 = np (1 - p ) Standard Deviation Example: Evans Electronics. What are the expected value, variance and standard deviation of the employees who will leave the company this year? 4
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1. E(c) = c 2. E(cx) = cE(x) 3. E(X + Y) = E(X) + E(Y) 4. E(X - Y) = E(X) - E(Y) 5. E(XY) = E(X)E(Y) , if X and Y are independent random variables Laws of Variance: 1. V(c) = 0 2. V(cX) = c
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ch5-6_notes - x MGMT 305 Business Statistics f(x)...

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