1. MATH104- Ch. 12 Statistics- part 1C Normal Distribution

2. Normal Distribution

3. Excerpt of Normal Chart– see p. 720 Z-scorepercentileZ-scorepercentile -4.00.0030.050.00 -3.00.130.569.15 -2.02.281.084.13 15.872.097.72 -0.530.853.099.87 4.099.997

4. Find the given probabilities Easiest examples P(z<1)= P(z<2)= P(z< -2)= P(z<1.5)=

5. Harder examples Recall P(z 1)= Recall P(z 2)= P(z>1.3)= P(z> -2.4)=

6. Find the given probabilities P( - 1<z<1)= P( -2<z<2)= P( -1.5<z<1.5)= P(1.4 < z < 2.3)= P( -1.8<z< 2.3)= P(- 2.1<z< -0.7)=

7. Normal Distribution Problems– Given x, find z, and then find P Example #1: Scores on a standardized test are normal with the mean = μ = 100 and the pop st dev = σ = 10. Create a normal curve to picture this example.

8. μ = 100, σ = 10 Find the probably that scores are: Lower than 100 Lower than 110 Greater than 110 Between 90 and 110 Between 80 and 120…

9. Continued… Find the probability that scores are: Lower than 115 Greater than 115 Lower than 108

10. Calculate z using the formula, and then find probability Lower than 93 Between 93 and 108 Hint: z =

11. Example #2-snowfall Assume snowfall amounts are normally distributed with mean μ =140, st dev = σ = 20. Find the probability that the amount is: Less than 180 inches Greater than 162 inches Between 134 and 174 inches

12. Ex 3: Heights- mean = 48, st dev= 4

13. Margin of error (p. 725)— if a statistic is obtained from a random sample of size n, there is a 95% probability that it lies within of the true populations statistic, where is called the margin of error. If 1100 people were surveyed about a politician, and 61% thought favorably of this person, the margin of error would be: So, there is a 95% probability that the true population percentage is between: