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Class 05. Using the Normal Intro to Descriptive Statistics

Class 05. Using the Normal Intro to Descriptive Statistics. EMBS Section 3.1, 3.2. and first part of 3.3. What we learned last class. To love the NORMAL distribution? IT IS FLEXIBLE Parameter μ lets you center it anywhere. Parameter σ lets you specify the width (variance, uncertainty)

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Class 05. Using the Normal Intro to Descriptive Statistics

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  1. Class 05. Using the NormalIntro to Descriptive Statistics EMBS Section 3.1, 3.2. and first part of 3.3

  2. What we learned last class • To love the NORMAL distribution? • IT IS FLEXIBLE • Parameter μ lets you center it anywhere. • Parameter σ lets you specify the width (variance, uncertainty) • If X is highly variable, pick a large σ • NORMDIST makes probability calculations easy. • No need for converting x to z in order to use the table in the book. No need for NORMSINV[(x-μ)/σ]. • It approximates the binomial when n is big • Just set μ=n*p and σ = [n*p*(1-p)]^.5

  3. EMBS Fig 6.4, p 249 You can’t make it skewed. You can’t change the 68/95/99 breakdown. It is a pdf (prob density function). The height is probability density. Areas under the curve are probabilities

  4. If X~N(μ,σ) And Y=a+b*X, Then Y~N(a+b*μ,b*σ) Temp(C)~N(10,10) Temp(F)= 32 + (9/5) Temp(C) Temp(F)~N(50,18) -20 -10 0 10 20 30 40 -4 14 32 50 68 86 104

  5. Case: Lorex Pharmaceuticals • Lorex produces Linatol (liquid medicine for high blood pressure) • Sold in 10-ounce bottles. • 600*12 = 7,200 fill attempts per shift • Linatol costs them $0.40 per ounce to make. • Bottles filled to more than 10 ounces get sold for $186 per case of 12. • Bottles under-filled get sold as seconds at a 20% discount ($148.8 per case)

  6. Case: Lorex Pharmaceuticals • The Filling Machine has an adjustable target. Test have shown that the fill amounts will be independent (across fill attempts) and • Normally distributed • μ = target • σ = 0.16 fluid ounces • In other words (symbols?) • X ~ N(target,0.16) What target should they use?

  7. Worksheets….

  8. Fill Test DataNormal(10.2,0.16)?

  9. Fill Test DataDescriptive StatisticsSummary Statistics

  10. Fill Test DataHistogram

  11. Assignment for class 06 • Find some numerical data • Get it into excel in one column with a label at the top • Data Analysis (File, Options, Addins, Go, check analysis ToolPak, okay) • Descriptive Statistics • Check “summary statistics” • One sheet • A brief description of the data and where you got it. • A printout (or hand copy) of the summary statistics • A brief answer to the question…could these data have come from a normal distribution…why or why not?

  12. Completed and extended worksheet

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