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Unformatted text preview: The Normal distributions PSLS chapter 11 © 2009 W.H. Freeman and Company Objectives (PSLS 11) The Normal distributions Normal distributions The 689599.7 rule The standard Normal distribution Using the standard Normal table (Table B) Inverse Normal calculations Normal distributions Normal curves are used to model many biological variables. They can describe the population distribution or density curve . Normal – or Gaussian – distributions are a family of symmetrical, bell shaped density curves defined by a mean μ ( mu ) and a standard deviation σ ( sigma ): N( μ,σ ). x x 2 2 1 2 1 ) (  = σ μ π x e x f Human heights, by gender, can be modeled quite accurately by a Normal distribution. 2 4 6 8 10 12 14 16 18 under 56 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 or more Height (inches) Percent Guinea pigs survival times after inoculation of a pathogen are clearly not a good candidate for a Normal model! 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 A family of density curves Here means are different ( μ = 10, 15, and 20) while standard deviations are the same ( σ = 3) Here means are the same ( μ = 15) while standard deviations are different ( σ = 2, 4, and 6). mean µ = 64.5 standard deviation σ = 2.5 N ( µ , σ ) = N (64.5, 2.5) The 68 – 95 – 99.7 rule for any N(μ, σ ) Reminder : µ (mu) is the mean of the idealized curve, while is the mean of a sample....
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This note was uploaded on 10/07/2011 for the course BSTT 400 taught by Professor Sallyfreels during the Fall '11 term at Ill. Chicago.
 Fall '11
 SallyFreels

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