MM_207_Seminar_6

MM_207_Seminar_6 - .9207.9222.9236.9251 Area to the left of...

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Unit 6 Seminar Normal Distributions MM207: Statistics

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LEARNING OUTCOMES Recognize the graph of a normal distribution Determine the area under the standard normal distribution curve Determine the area under any normal distribution curve Calculate probabilities of random variables with normal distributions
Normal Distribution An example of continuous probability

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Raw score: the actual value Z-score: the number of SD of the raw score from the mean A normal distribution has µ = 5 and σ = 1.5. Find z for x = 2.5. σ μ - = - = x SD mean score raw z
Standard Normal Distribution A normal distribution with Mean = 0 Standard Deviation = 1 Normal Standard Normal by converting x-values to z values (or z scores) Use the Standard Normal distribution to find the area under the curve

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Area Under Curve z .00 .01 .02 .03 .04 -2.7 .0035 .0034 .0033 .0032 .0031 1.4 .9192

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Unformatted text preview: .9207 .9222 .9236 .9251 Area to the left of 2.71 is 0.0034 Area to the right of 1.44 is 0.9251 Area between -2.71 and 1.44 is 0.9251 – 0.0034 = 0.9217 Use a standard normal distribution table to find the area under the curve between z = –1.08 and z = 2.13. Answer: 0.8433 Probability & Std. Norm. Dist. • Let x have a normal distribution with µ = 13 and σ = 3. – Find the probability that an x value selected at random from this distribution is between 8 and 16. • P(8 ≤ x ≤16) • P(-1.67 ≤ z ≤ 1) • P (z ≤ 1) – P (z ≤ -1.67) • 0.8413 - 0.0475 • Answer: 0.7938 Example • Find z such that 81% of the area under the standard normal curve lies between – z and z . • Answer: 1.31 Example • Find z so that 3.5% of the standard normal curve lies to the right of z . • Answer: 1.81...
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MM_207_Seminar_6 - .9207.9222.9236.9251 Area to the left of...

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