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Lecture 6

Bio2244 Lecture 6,7 and 8.docx

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Biology 2244A/B
Angela White

Lecture 6,7,8 Normal Distribution - Graph must be symmetric, and bell-shaped with mean in the center - Uniform distribution o Rectangular graph o Each value has an equal probability - Density curve o Continuous distribution o requirements  Area under curve = 1  All points on curve must be greater than or equal to zero STANDARD NORMAL DISTRIBUTION - Area under curve = probability - Requirements o Mean = 0, SD = 1, AUC = 1 - area under curve o calculated using Z-SCORE TABLE  ONLY FINDS CUMULATIVE PROPABILITIES FROM THE LEFT SIDE o 1 tailed – DIRECTIONALITY o 2 tailed – NO DIRECTIONALITY o If you know probability, work in reverse to find Z-score  KNOW WHICH AREA UNDER CURVE THE PROBABILITY IS REFERRING TO Applications – Z-SCORE IS NOT AREA - If a graph is nonstandard (ie. Mean doesn’t equal zero and SD isn’t one) o Use Z = x-mean/sigma TWO DECIMALS  Standardizes scores  Process  Make nonstandard graph  Shade region required by question  Convert x-values required into Z-scores  Find the probabilities and answer the question o Z-score  Is not area  Choose the right side of graph  Negative z-score on left side of distribution  Areas are never negative o Can use SD, probability and mean to find X  Use probability to find z-score  Use standardizing z-score formula to find X Sampling Distributions - Know difference between population SD and sample SD - Why do we sample with replacement? o Small samples from big populations don’t make a big difference with or without replacement o Makes events independent - Sampling distribution of the mean o Probability distribution o All samples have same sample size n o FIND MEANS within each sample
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