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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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Box and Whiskers with Outliers. Outlier…… An extremely high or an extremely low value in the data set when compared with the rest of the values. The IQR.

Box and Whiskers with Outliers. Outlier…… An extremely high or an extremely low value in the data set when compared with the rest of the values. The IQR.

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