Slide 1Test 3 ResultsPractice ProblemsAdditional Reading and ExamplesTest 4Slide 6Properties of the Normal DistributionNotationSlide 9Standard Normal DistributionNormal TableTypes of ProblemsRefresher ProblemsRefresher ProblemsRefresher ProblemsRefresher ProblemsRefresher ProblemsNormal VariablesNormal VariablesZ-Score TransformationZ-Score TransformationZ-Score TransformationZ-Score TransformationExample 47Example 47Example 47Example 47Example 47Example 48Example 48Example 48Example 48Practice ProblemsPractice Problem AnswersStandard Normal DistributionLess Than ProblemLess Than ProblemLess Than ProblemFinding Values of ZTI-83/84 CalculatorExample 42Example 42Example 42Example 42Example 43Example 43Example 43Example 43Greater Than ProblemGreater Than ProblemGreater Than ProblemGreater Than ProblemExample 44Example 44Example 44Example 44Example 45Example 45Example 45Example 45Between ProblemBetween ProblemBetween ProblemBetween ProblemBetween ProblemBetween ProblemBetween ProblemBetween ProblemExample 46Example 46Example 46Example 46Example 46Example 46Example 46Example 46Normal VariablesZ-Score TransformationZ-Score TransformationZ-Score TransformationZ-Score TransformationZ-Score TransformationExample 49Example 49Example 49Example 49Example 49Example 49Example 49Example 50Example 50Example 50Example 50Example 50Example 50Example 50Example 50Slide 98STAT 210Lecture 20Normal DistributionsOctober 12, 2016Test 3 ResultsMean: 85.8 Median: 94.0Max: 100 Min: 23 n: 136Score Frequency Relative Frequency90’s 78 57.35%80’s 26 19.12%70’s 11 8.09%60’s 10 7.35% <60 11 8.09%Practice ProblemsPages 162 through 165Relevant problems: VI.4Recommended problems: VI.4Additional Reading and ExamplesRead pages 158 through 160Test 4Wednesday, October 19Questions 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 questions and problems.Formulas provided; Bring a calculator!Practice Tests and Formula Sheet on Blackboard.ClickerProperties of the Normal Distribution•The normal curve is bell-shaped•The peak of the curve is the population mean m•The normal curve is symmetric about m•The center and spread are completely described by specifying the values of the population mean m and the population standard deviation s•The total area under the normal curve is 1 (or 100%)NotationX ~ N (m , s)“X is distributed normal with mean m and standard deviation s”ClickerStandard Normal Distribution•Denoted by Z•Has population mean m = 0 (center)•Has population standard deviation s = 1 (spread)•Shape is normal (symmetric bell curve)•No unusual features•Z ~ N(0, 1)•Probabilities are tabled on pages 338 - 339Normal TableGives the probability that the standard normal variable Z falls below some specified value z (less than problems).Read the value of z down the left-most column and across the top row, and read the probability from the body of the table.Types of Problems1. Given values of the variable X, find the probability (or area or proportion or percentage).2. Given a probability (or area or proportion or percentage), find the value of the variable X.Refresher Problems1. Find the probability that the standard normal variable Z equals -3.12. P(Z = -3.12) = CLICKER2. Find the probability that the standard normal variable Z takes the value 2.13 or less. P(Z < 2.13) = ???3. Find the probability that the standard normal variable Z takes the value -0.58 or more. P(Z > -0.58) = ???4. Find the probability that the standard normal variable Z takes a value between -1.59 and 0.44.P(-1.59 < Z < 0.44) = ???Refresher Problems1. Find the probability that the standard normal variable Z equals -3.12. P(Z = -3.12) = 02. Find the probability that the standard normal variable Z takes the value 2.13 or less. P(Z < 2.13) = ???3. Find the probability that the standard normal variable Z takes the value -0.58 or more. P(Z > -0.58) = ???4. Find the probability that the standard normal variable Z takes a value between -1.59 and 0.44.P(-1.59 < Z < 0.44) = ???Refresher Problems1. Find the probability that the standard normal variable Z equals -3.12. P(Z = -3.12) = 02. Find the probability that the standard normal variable Z takes the value 2.13 or less. P(Z < 2.13) = .9834Calculator: normalcdf(-1E99, 2.13, 0, 1)3. Find the probability that the standard normal variable Z takes the value -0.58 or more. P(Z > -0.58) = ???4. Find the probability that the standard normal variable Z takes a value between -1.59 and 0.44.P(-1.59 < Z < 0.44) = ???Refresher Problems1. Find the probability that the standard normal variable Z equals -3.12. P(Z = -3.12) = 02. Find the probability that the standard normal variable Z takes the value 2.13 or less. P(Z < 2.13) = .98343. Find the probability that the standard normal variable Z takes the value -0.58 or more. P(Z > -0.58) = 1 – P(Z < -0.58) = 1 - .2810 = .7190Calculator: normalcdf(-0.58, 1E99, 0, 1)4. Find the probability that the standard normal variable Z takes a value between -1.59 and 0.44.P(-1.59 < Z < 0.44) = ???Refresher Problems1. Find the probability that the standard normal variable Z equals -3.12. P(Z = -3.12) = 02. Find the probability that the standard normal variable Z takes the value 2.13 or less. P(Z < 2.13) = .98343. Find the probability that the standard normal variable Z takes the value -0.58 or more. P(Z > -0.58) = 1 – P(Z < -0.58) = 1 - .2810 = .71904. Find the probability that the standard normal variable Z takes a value between -1.59 and 0.44.P(-1.59 < Z < 0.44) = P(Z < 0.44) – P(Z < -1.59) = .6700 - .0559 = .6141 Calculator: normalcdf(-1.59, 0.44, 0, 1)Normal VariablesA standard normal (Z) distribution requires that the mean is 0 and that the standard deviation is 1.How many real variables (weight, height, grades on a test, etc.) do you think have a mean of 0 and a standard deviation of 1?ClickerNormal VariablesA standard normal (Z) distribution requires that the mean is 0 and that the standard deviation is 1.How many real variables (weight, height, grades on a test, etc) do you think have a mean of 0 and a standard deviation of 1?Answer: I cannot think of any!Z-Score TransformationSkip to page 147Suppose X is distributed normal with some mean m not equal to 0 and/or some standarddeviation
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