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

MATH104- Ch. 12 Statistics- part 1C Normal Distribution. Normal Distribution. Excerpt of Normal Chart– see p. 720. Find the given probabilities. Easiest examples P(z<1)= P(z<2)= P(z< -2)= P(z<1.5)= . Harder examples. Recall P(z<1)= Try P(z>1)= Recall P(z<2)= Try P(z>2)=

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

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  1. MATH104- Ch. 12 Statistics- part 1CNormal Distribution

  2. Normal Distribution

  3. Excerpt of Normal Chart– see p. 720

  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)= Try P(z>1)= • Recall P(z<2)= Try 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:

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