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10-17-07 - according to rules of probabilities Probability...

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Standard Normal Tables An internal probability distribution gives probability that random variable, X, will be between to given values. P(x 1 < X < x 2 ) P(Z < z) … z will take on some value less than z P(z 1 < Z < z 2 ) = P(Z < z 2 ) – P(Z<z) Steps in Solving Normal Probability Problems 1. Write down information about random variable i.e. x 2 (μ,σ) 2. Draw picture of problem and write down the probability statement. Ex. P(x>30) 3. Transform value of X into Z values. Example 3.22 μ = $350 σ = $240 P(z) = $4000 Z = 4000 – 3500 = 2.08 240 (Go to the Table) P(z>4000) = 1-P(z<4000) = 1-.98 = .0188 or 18.8% General Addition Rule P(A or B) = P(A) + P(B) – P(A&B) Conditional Probability P(A or B) = P(A&B) General Multiplication Rule P(A&B) = P(A or B) x P(B) Statistical Independence If A&B are independent: P(A&B) = P(A) x P(B) Or P(A/B) = P(A)
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Parameters When Purchase will be made a) P(a) = b) P(b) = 90 + 530 – 56 = 564 = 58% 978 978 c) 34 + 156 = 190 978 978 Random Variables – a random variable is a quantitative variable whose value varies
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Unformatted text preview: according to rules of probabilities Probability Distribution of Random Variables The probability distribution of random variable x, p(a) gives the probability that the random variable will take on each of possible values. Sampling Distribution and Confidence Interval Point Estimators Biased Sample – does not represent all characteristics of population Point Estimate vs. Interval Estimate μ σ Statistic – describes sample Parameter – describes population Point Estimates Mean, standard deviation, mode, and median. μ v/x Type of Computer 0-3m 3-6m 6-12m Total Notebook 34 15 258 448 Desktop 56 346 128 530 Total 90 592 386 978 σ S Point estimate for quantitative variables. Comparing two populations… Comparing mean and variances… __ __ μ 1 – μ 2 X 1 – X 2 Common Point Estimator σ 1 2----- = 1 σ 2 1...
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