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Unformatted text preview: Numerical Examples for Statistical Tables The presentation of the statistical tables is not universal. Some statistical textbooks authors’ enjoy given tabular values of the righttail probabilities, while for others lefttail probabilities are preferred. Even within each of these groups you will find some differences in presenting each table differently than others, never in a unified format. This lack of uniformity often confuses most of students while learning statistics. The following presents some numerical examples of common statistical tables with some applications. You may like using The Pvalues for the Popular Distributions JavaScript. Binomial Probability X ∼ B(n, p), read, the random variable X has a binomial distribution with parameters n trials, and probability of a success is p. Example: Find probability of at most k = 3 success from B(n = 7, p = 0.4). Using any Binomial table, one should get: P[k ≤ 3] = 0.7102. Using The Pvalues for the Popular Distributions JavaScript, one gets: P[k ≤ 3] = 1 – P[k ≥ 4] = 1 – 0.2898 = 0.7102. Questions for you: Which of the following two events is more likely to happen? Getting exactly 6 heads in tossing a fair coin (i.e., p=1/2), n = 10 times or tossing it n=20 times. Why? Application: A traveling salesman has found that the probability of a sale on a single contact is 0.02. If the salesman contacts 200 prospects, find the probability that he will make at least one sale. P[at least one sale] = 1 – P[no sale] = 1 – (10.02) 200 = 1 – (0.98) 200 = 98% Normal Density Function X ∼ N(0, 1), read, the random variable X is distributed Normally with mean, and variance 0, and 1, respectively. A Fact: If X ∼ N( μ, σ ), then Ζ = (X μ29 / σ ∼ N(0, 1) Example: Let X ∼ N(1, 2), compute P(X ≤ 5.21) P [ (X  1) / 2 ≤ (5.21  1) / 2 ] = P(Z ≤ 2.105) ≈ P(Z ≤ 2.11) = .4826 + .5 = .9826 Notice that P(Z ≤ 0) = .5 Similarly, P(X ≥ 2.1) = P(Z ≥ (2.1 1) / (2)) = P(Z ≥ .55) = 0.5  .2088 = .2912 Using The Pvalues for the Popular Distributions...
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 Spring '08
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