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Unit 4 – Probability and Statistics Section 12.7 Day 10

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Warm-Up Using the given data set: 77, 76, 83, 88, 90, 85, 81, 77, 95, 89 1. Find the mean, median, mode 2. Find the range and interquartile range 3. Create a box-and-whisker plot of the data 4. Find the standard deviation (Show all your work.)

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Warm-Up Answers Data set in order: 76, 77, 77, 81, 83, 85, 88, 89, 90, 95 1. Mean = 84.1; Median = 84 ; Mode = 77 2. Range = 19; Interquartile range = 12 3. Create a box-and-whisker plot of the data 4. Standard deviation σ = 6.1

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Section 12.7 Normal Distributions Goal: calculate probabilities using normal distributions Normal Curve – symmetrical bell-shaped curve Important symbols σ (Sigma) represents standard deviation x (x-bar) represents mean

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Section 12.7 Normal Distributions Important Aspects of a Normal Curve Total Area under the curve is 1 68% of the area lies within 1 standard deviation of the mean 95% of the area lies within 2 standard deviations of the mean 99.7% of the area lies within 3 standard deviations of the mean

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Section 12.7 Normal Distributions x +σ+σ+2σ+3σ-σ-σ-2σ-3σ 34% 13.5% 2.35% 13.5% 0.15%

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Example 1 The price of sandals is normally distributed with a mean of $36 and a standard deviation of $9. A) What percent were priced between $18 and $72? B) What is the probability that a randomly chosen pair is priced between $9 and $18?

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Example 1 (cont.) $36 $45$54$63$27$18$9 34% 13.5% 2.35% 13.5% 0.15% A) What percent were priced between $18 and $72? 97.5%

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Example 1 (cont.) $36 $45$54$63$27$18$9 34% 13.5% 2.35% 13.5% 0.15% B) What is the probability that a randomly chosen pair is priced between $9 and $18? 2.35%

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Example 2 The weight of strawberries packed in a medium-sized container was normally distributed with a mean of 16.18 ounces and a standard deviation of 0.34 ounce. A) If you randomly choose 2 containers of strawberries, what is the probability that both weigh less than 15.5 ounces? B) If you randomly choose 2 containers of strawberries, What is the probability that both of the containers weighs at least 15.84 ounces? C) If you randomly choose 2 containers of strawberries, that one container weighs between 15.5 and 15.84 ounces, and the 2 nd container weighs at least 16.86 ounces?

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Example 2 (cont.) 16.1816.5216.8617.215.8415.515.16 34% 13.5% 2.35% 13.5% 0.15% (oz.) A) Both containers weigh less than 15.5 oz? 0.025 0.025 = 0.000625 or 0.0625%

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Example 2 (cont.) 16.1816.5216.8617.215.8415.515.16 34% 13.5% 2.35% 13.5% 0.15% (oz.) B) Both containers weigh at least 15.84 oz? 0.84 0.84 = 0.7056 or 70.56%

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Example 2 (cont.) 16.1816.5216.8617.215.8415.515.16 34% 13.5% 2.35% 13.5% 0.15% (oz.) C) Between 15.5 and 15.84 oz and at least 16.86? 0.135 (0.0235 +.0015) = 0.003375 or 0.3375%

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PRACTICE P. 749-750 #19 - 28

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PRACTICE ANSWERS 19) 50% 20) 15.85% 21) 2.5% 22) 27% 23) 0.68 24) 0.4985 25) 0.9735 26) 0.84 27) 0.84 28) 0.975

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HOMEWORK P. 750-751 #29 – 31, 38 - 49

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