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Warm Up

Warm Up. A normal distribution has a mean of 64 and a standard deviation of 3. Find the probability that a randomly selected value from the distribution is in the interval. Less than 64 Between 61 and 70 Greater than 67 Less than 61 or greater than 73. Homework Review. 2. 2.5 4. 9.46

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Warm Up

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  1. Warm Up • A normal distribution has a mean of 64 and a standard deviation of 3. Find the probability that a randomly selected value from the distribution is in the interval. • Less than 64 • Between 61 and 70 • Greater than 67 • Less than 61 or greater than 73

  2. Homework Review 2. 2.5 4. 9.46 6. 16% 5. 5 scores 7. 3.6 2.9 31 10. 68 [105, 145]

  3. Math II BDay 2 (1-5-11) • Standard MM2D1C • Use means and standard deviations to compare data sets • Today’s Question: • How do we use standard deviation to compare data sets?

  4. Cat and Whisker to Bell Curve Total area under the curve is 100%

  5. Empirical Rule

  6. Is this population – normal? 4 6 8 12 9 7 5 4 3 2

  7. N = Mean = Range = Variance = Standard Deviation = 60 4.82 4 6 8 12 9 7 5 4 3 2 10 - 1 = 9 5.34 2.31

  8. How many Data Points are ± 1 Std. Deviation • Mean ± 1 Std. Deviation • 4.82 + 2.31 = 7.13 • 4.82 – 2.31 = 2.51 2.51 7.13 8 12 9 7 5

  9. Total count between the Std Deviation Lines • 8 + 12 + 9 + 7 + 5 = 41 • Count Between Lines / Total N • 41/60 = .6833 = 68.33% • Compare to Empirical Rule • 68.33% ≈ 68%

  10. How many Data Points are ± 2 Std. Deviation • Mean ± 2 Std. Deviation • 4.82 + (2)2.31 = 9.44 • 4.82 – (2)2.31 = 0.20 0.20 9.44 4 6 8 12 9 7 5 4 3

  11. Total count between the Std Deviation Lines • 4 + 6 + 8 + 12 + 9 + 7 + 5 + 4 + 3= 58 • Count Between Lines / Total N • 58/60 = .9667 = 96.67% • Compare to Empirical Rule • 96.77% ≈ 95%

  12. How many Data Points are ± 3 Std. Deviation • Mean ± 3 Std. Deviation • 4.82 + (3)2.31 = 11.75 • 4.82 – (3)2.31 = -2.11 -2.11 11.75 4 6 8 12 9 7 5 4 3 2

  13. Total count between the Std Deviation Lines • 4 + 6 + 8 + 12 + 9 + 7 + 5 + 4 + 3 + 2 = 60 • Count Between Lines / Total N • 60/60 = 1.00 = 100% • Compare to Empirical Rule • 100% ≈ 99.7%

  14. Is this population – normal? Possibly

  15. Get into your groups of 2 Do the Task #4

  16. Homework Pg 267 # 1 - 11

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