Math Models Unit 3 Lesson 6

11. The lifetime for a certain type of battery has been shown to be 2 years (the mean) with a standard deviation of 4 months. In a normal distribution, what percentage of these batteries will last more than 2 years and 8 months? : 2%

In a normal distribution, what percentage of these batteries will last between 1 year and 8 months and 2 years and 4 months, within one standard deviation of the mean? : 68%

9. Use your calculator to find the mean, x̄, and the standard deviation, σ, rounded to the nearest hundredth. {- 1, - 1.35, - 0.95, 0.5, 0, - 0.75, 0.25}

x̄ = -0.47 σ = 0.66

10. Use your calculator to find the mean, x̄, and the standard deviation, σ, rounded to the nearest hundredth. {0.1, 0.5, 0.02, 0.1, 0.2, 0.05, 0.3, 0.03, 0.02, 0.3, 0.2, 0.1, 0.5, 0.6}

x̄ = 0.22 σ = 0.19

8. Use your calculator to find the mean, x̄, and the standard deviation, σ, rounded to the nearest hundredth. {0.01, 0.09, 0.9, 0.03, 0.025, 0.85, 0.04, 0.4}

x̄ = 0.29 σ = 0.36

6. Use your calculator to find the mean, x̄, and the standard deviation, σ, rounded to the nearest hundredth. {2.25, 1.25, 3.75, 3.5, 2.5, 4, 3, 2, 1.75}

x̄ = 2.67 σ = 0.90

7. Use your calculator to find the mean, x̄, and the standard deviation, σ, rounded to the nearest hundredth. {90, 56, 75, 87, 98, 69, 72, 74, 83, 81, 81}

x̄ = 78.73 σ = 10.82

4. Find the standard deviation by completing the table. n = the number of data poìnts = 13 ∑x = 26 x̄ = ∑x/n = 2

∑(x - x̄)² = 10 ∑(x - x̄)² /n = s² = o² = 0.769 √∑(x - x̄)² / n = s = 0.876

3. Find the standard deviation by completing the table. n = the number of data poìnts = 16 ∑x = 1248 x̄ = ∑x/n = 78

∑(x - x̄)² = 2198 ∑(x - x̄)² /n = s² = o² = 137.38 √∑(x - x̄)² / n = s = 11.72

5. Find the standard deviation by completing the table. n = the number of data poìnts = 9 ∑x = -27 x̄ = ∑x/n = -3

∑(x - x̄)² = 22 ∑(x - x̄)² /n = s² = o² = 2.44 √∑(x - x̄)² / n = s = 1.56

2. Find the standard deviation by completing the table. n = the number of data poìnts = 13 ∑x = 169 x̄ = ∑x/n = 13

∑(x - x̄)² = 48 ∑(x - x̄)² /n = s² = o² = 3.69 √∑(x - x̄)² / n = s = 1.92

1. Find the standard deviation by completing the table. n = the number of data poìnts = 12 ∑x = 60 x̄ = ∑x/n = 5

∑(x - x̄)² = 58 ∑(x - x̄)² /n = s² = o² = 4.83 √∑(x - x̄)² / n = s = 2.20

12. What is the formula to calculate mean?

∑x/n