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Recall: The percentile is the % of data less than a given value (e.g. Z‐score). The Zscore of a value is the number of standard deviations that a value is away from the mean. Z = 0.37 corresponds to being 0.37 σ to the left of the mean. Apr 158:14 AM Using Percentiles to Calculate % between values Ex: Given Q ~ N(7, 2.22), find the percent of data in the interval 3 < q < 6. Find Zscores of 3 and 6 Find the corresponding percentiles for Zscores of 3 and 6 Subtract Percentile associated with 3 from Percentile associated with 6 Z‐score for q =3, Z‐score for q =6, Percentile for Z = ‐1.8 Percentile for Z = ‐0.45 percentile Subtract the percentiles to determine the percentage between the two z‐scores. Therefore, 29% of the data is within the range 3<q<6 for this given distribution. Apr 156:55 AM 1 You try! Given a normal distribution of values for which the mean is 70 and the standard deviation is 4.5, find: a) the percentage of values between 65 and 80. b) the percent of values greater than 75. c) the probability that a value is less than 62. d) the 90th percentile for this distribution. We want to know the X value that corresponds to the 90th percentile. Apr 156:55 AM Ex. but this time on graphing calculator Given a normal distribution of values for which the mean is 70 and the standard deviation is 4.5, find: a) the percentage of values between 65 and 80, inclusive. normalcdf(lower,upper,mean,SD) normalcdf(65,80,70,4.5) b) the percent of values greater than 75. the graphing calculator can't handle infinity ... so the upper bound is 1 x 1099 (1 EE 99) normalcdf(75,1x1099,70,4.5) key in: c) the probability that a value is less than 62. normalcdf(‐1x1099,62,70,4.5) key in: d) the value which corresponds to the 90th percentile for this distribution. Command: invNorm(value,mean,SD) invNorm(0.90,70,4.5) = 75.77 Compare the values computed using the graphing calculator to those we calculated using the Zscore tables. Which one is more accurate? Apr 158:27 AM 2 Computing Z‐Scores Using the TI‐83 Graphing Calculator Given N(x,σ2): To determine the percentage of total data between two numbers a and b,(a < x < b): Note: a can be ‐1x1099 for ‐infinity b can be +1x1099 for +infinity 1) access the normalcdf function normalcdf(a,b,μ,σ) 2) enter relevant data 3) multiply computed value by 100% To determine the value of the nth percentile 1) access the invNorm function 2) enter relevant data invNorm(n,μ,σ) Graphing calc HW: pg 186 Do with one method, verify with the other. # 9, 10, 12, 13, 14, 15, 17 Oct 265:23 PM 3