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
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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
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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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