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Advanced Alg – Unit 1

Advanced Alg – Unit 1. Z - Scores. Review. Data collection from the Math IV Survey gave a mean of 25 and a standard deviation of 5. What percent of the data is below 35?. Z Score. z score =. Data – Mean σ (round to two decimal places) σ : standard deviation

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Advanced Alg – Unit 1

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  1. Advanced Alg– Unit 1 Z - Scores

  2. Review Data collection from the Math IV Survey gave a mean of 25 and a standard deviation of 5. What percent of the data is below 35?

  3. Z Score z score = Data – Mean σ (round to two decimal places) σ: standard deviation Gives exact standard deviation of a piece of data.

  4. Find the z score Given: Data = 93 Mean = 90 σ = 2 z score = (93 – 90) ÷ 2 = 1.50 1.5 σ above the mean

  5. Find the z score Given: Data = 80 Mean = 90 σ = 2 z score = (80 – 90) ÷ 2 = -5.00 5 σ below the mean

  6. Using Z – Scores to find Probability

  7. Using the Chart to find Probability Steps Find Z – Score Find first part of Z-score at Column. Find the second part at the top Row Use these to find probability above (In decimal form).

  8. Find probability for a z-score of 0.31 A z-score of 0.31give a probability of .6217 or 62%

  9. Find probability for a z-score of 0.25 A z-score of 0.25 give a probability of .5987 or 60%

  10. Find probability for a z-score of 0.04 A z-score of 0.04 give a probability of .5160 or 52%

  11. Find the probability given: Mean: 30 σ = 5 Score: 36 z-score = (36 – 30) ÷ 5 = 1.20 z-score of 1.20 = .8849 88.49%

  12. Find the probability given: Mean: 55 σ = 6 Score: 40 z-score = (40 – 55) ÷ 6 = -2.50 z-score of -2.50 = .0062 .62%

  13. Find the probability given: Mean: 120 σ = 13 Score: 130 z-score = (130 – 120) ÷ 13 = 0.77 z-score of 0.77 = .7794 77.94%

  14. Find the probability above given: Mean: 68 σ = 10 Score: 50 z-score = (50 – 68) ÷ 10 = -1.80 z-score of -1.80 = .0359 100 - 3.59% = 96.41%

  15. Question 55% below gives what % above? 45 47% below gives what % above? 53

  16. Find the data that will give z-score Steps Use percent to find z-score Find mean and σ Plug into formula and solve for data

  17. Given: Mean of 96 and σ = 7Find: Find data that shows less that 72% 72% = a z-score of .58 .58 = (D – 96)/ 7 7(.58) = D – 96 4.06 = D – 96 D = 4.06 + 96 D = 100.06

  18. Given: Mean of 96 and σ = 7Find: Find data that shows less that 20% 20% = a z-score of -.84 -.84 = (D – 96)/ 7 7(-. 84) = D – 96 -5.88 = D – 96 D = -5.88 + 96 D = 90.12

  19. Given: Mean of 96 and σ = 7Find: Find data that shows less that 98% 98% = a z-score of 2.05 2.05 = (D – 96)/ 7 7(2.05) = D – 96 14.35 = D – 96 D = 14.35 + 96 D = 110.35

  20. Given: Mean of 96 and σ = 7Find: Find data that shows less that 72% 72% = a z-score of .68 .58 = (D – 96)/ 7 7(.58) = D – 96 4.06 = D – 96 D = 4.06 + 96 D = 100.06

  21. Percent between Mean = 50, Standard Deviation = 5 What percent is between 42 and 61? Z-score for 42 = -1.60 → 5.48% Z-score for 61 = 2.20 → 98.61% Between = 98.61 – 5.48 = 93.13%

  22. Percent between Mean = 100, Standard Deviation = 23 What percent is between 110 and 130? Z-score for 110 = 0.43 → 66.64% Z-score for 130 = 1.30 → 90.32% Between = 90.32 – 66.64 = 23.68%

  23. Percent between Mean = 44, Standard Deviation = 6 What percent is between 42 and 51? Z-score for 42 = -0.33 → 37.07% Z-score for 61 = 0.74 → 77.04% Between = 77.04 – 37.07 = 39.97%

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