VCU STAT 210  Lecture22(2) (1) (56 pages)
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Lecture22(2) (1)
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 56
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 Virginia Commonwealth University
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 Stat 210  Basic Practice of Statistics
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STAT 210 Lecture 22 Normal Distributions t Distributions and Sampling Distributions October 17 2016 Practice Problems Pages 162 through 165 Relevant problems VI 16 and VI 17 Recommended problems VI 16 and VI 17 Additional Reading and Examples Read pages 158 through 160 Test 4 Wednesday October 19 Questions for the first 10 minutes then test papers due promptly at the end of class Covers chapter 6 pages 139 168 Combination of multiple choice questions and written short answer problems Formulas and Z table provided Bring a calculator Practice Tests and Formula Sheet on Blackboard Clicker Z Score Transformation Suppose X is distributed normal with some mean m not equal to 0 and or some standard deviation s not equal to 1 X N m s Z Score Transformation For a problem that asks to find a probability we convert to a standard normal variable Z N 0 1 Z X m value mean s standard deviation Then find the probability for Z using the normal table Z Score Transformation X N m s Z X m s Suppose we want to find the value x such the probability of being in some interval is as specified Z Score Transformation 1 Find the value z that satisfies the probability 2 Then calculate x by substituting into the following formula X m Zs Steps for Solving 1 Identify the variable X 2 Write out the distribution X N m s 3 Determine the type of problem probability or value 4 Solve the problem 5 Make sure the answer makes sense Clicker Example 51 X time people stir sugar into their iced tea X N 12 3 3 1 Find P 19 833 X 22 53 Example 51 X time people stir sugar into their iced tea X N 12 3 3 1 Find P 19 833 X 22 53 P 19 833 12 3 Z 22 53 12 3 3 1 3 1 P 2 43 Z 3 30 Example 51 X time people stir sugar into their iced tea X N 12 3 3 1 Find P 19 833 X 22 53 P 19 833 12 3 Z 22 53 12 3 3 1 3 1 P 2 43 Z 3 30 P Z 3 30 P Z 2 43 Example 51 X time people stir sugar into their iced tea X N 12 3 3 1 Find P 19 833 X 22 53 P 19 833 12 3 Z 22 53 12 3 3 1 3 1 P 2 43 Z 3 30 P Z 3 30 P Z 2 43 9995 9925 Example 51 X time people stir sugar into their iced tea X N 12 3 3 1 Find P 19 833 X 22 53 P 19 833 12 3 Z 22 53 12 3 3 1 3 1 P 2 43 Z 3 30 P Z 3 30 P Z 2 43 9995 9925 007 Example 51 X time people stir sugar into their iced tea X N 12 3 3 1 Find P 19 833 X 22 53 P 19 833 12 3 Z 22 53 12 3 3 1 3 1 P 2 43 Z 3 30 P Z 3 30 P Z 2 43 9995 9925 007 Calculator normalcdf 19 833 22 53 12 3 3 1 Example 52 X weight of leatherback turtle X N 760 98 Find the weight of a turtle such that the turtle falls in the bottom 20 of the distribution Example 52 X weight of leatherback turtle X N 760 98 Find the weight of a turtle such that the turtle falls in the bottom 20 of the distribution Find the value of X such that the probability of being less than this value is 20 Example 52 X weight of leatherback turtle X N 760 98 Find the value of X such that the probability of being less than this value is 20 1 z P Z z 20 Example 52 X weight of leatherback turtle X N 760 98 Find the value of X such that the probability of being less than this value is 20 1 z P Z z 20 2 3 Find p 20 in the body of the table read across and up to find z 0 84 Example 52 X weight of leatherback turtle X N 760 98 Find the value of X such that the probability of being less than this value is 20 1 z P Z z 20 2 3 Find p 20 in the body of the table read across and up to find z 0 84 x m zs 760 0 84 98 760 82 32 Example 52 X weight of leatherback turtle X N 760 98 Find the value of X such that the probability of being less than this value is 20 1 z P Z z 20 2 3 Find p 20 in the body of the table read across and up to find z 0 84 x m zs 760 0 84 98 760 82 32 677 68 Example 52 X weight of leatherback turtle X N 760 98 Find the value of X such that the probability of being less than this value is 20 1 z P Z z 20 2 Find p 20 in the body of the table read across and up to find z 0 84 x m zs 760 0 84 98 760 82 32 677 68 The turtle would have to weight 677 68 pounds or less Example 53 X miles per gallon for new Pontiac G6 s that Oprah gave away on her September 13 2004 show X N 26 3 3 6 Example 53 X miles per gallon for new Pontiac G6 s that Oprah gave away on her September 13 2004 show X N 26 3 3 6 Find the miles per gallon to be in the top 20 19 of the distribution Clicker Example 53 X miles per gallon for new Pontiac G6 s that Oprah gave away on her September 13 2004 show X N 26 3 3 6 Find the miles per gallon to be in the top 20 19 of the distribution Find the value x such that the miles per gallon is in the top 20 19 of the distribution Example 53 X miles per gallon for new Pontiac G6 s that Oprah gave away on her September 13 2004 show X N 26 3 3 6 Find the value x such that the miles per gallon is in the top 20 19 of the distribution 1 z P Z z 2019 2 z P Z z 1 2019 7981 3 Find p 7981 in the body of the table read across and up to find z 0 83 or z 0 84 Example 53 X miles per gallon for new Pontiac G6 s that Oprah gave away on her September 13 2004 show X N 26 3 3 6 Find the value x such that the miles per gallon is in the top 20 19 of the distribution 1 z P Z z 2019 2 z P Z z 1 2019 7981 3 Find p …
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