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# STATSWeekSevenNotes.pdf Stats 1350

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This 8 page Class Notes was uploaded by Alyssa Leathers on Friday February 27, 2015. The Class Notes belongs to Stats 1350 at Ohio State University taught by Ali Miller in Winter2015. Since its upload, it has received 104 views.

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Date Created: 02/27/15

STATS 1350 22615 126 PM Week Seven Chapter 13 Normal Distributions Symmetric vs Skewed Normal Curves Perfectly symmetric about mean 0 One standard deviation is about one halfway up 0 Doesn t ever touch zero Notation for Normal Distribution mu this is the symbol for the MEAN of the distribution the mean is in the center of the distribution 0 sigma this is the symbol for the STANDARD DEVIATION tells disperse or deviate value ZScore Standardized value zscore formula 0 Z observation mean standard deviation X data mu sigma of standard deviations that x is away from the mean 0 Example 0 Jacob scores 16 on the ACT normally with mean of 208 mu and standard deviation of 48 sigma 0 Emily scores 670 on the SAT normally with mean of 1026 mu and standard deviation of 209 sigma Who s doing better need to compare zscores X 16670 Mean 2081026 Standard Deviation 48209 Zscore 1620848 1 and 6701026209 17 Jacob was 1 standard deviation below the mean but Emily was 17 standard deviations below the mean 0 Relative to group Emily scored worse on SAT she s farther from mean OOOOOO Example 0 Mean 80 mu 0 Standard deviation 10 sigma 0 Observation 90 x o 908010 1 zscore o 1 standard deviation from mean Bellshaped curve features 6895997 Rule Empirical Rule 0 68 of the observation fall within 1 standard deviation sigma of the mean 0 Z between 1 and 1 95 of the observations fall within 2 standard deviations Zsigma of the mean 0 Z between 2 to 2 o 997 of the observations fall within 3 standard deviations 3sigmas of the mean 0 Z between 3 and 3 The total area under the curve is 100 0 Give sense for where data is at 0 Pictures 0 Never touches zero 0 Drawing 015 235 135 34 34 135 235 01500 Empirical Rule Example 0 Mean 1325 0 Standard Deviation 25 0 Middle 68 o 1325 25 1325 25 1300 1350 Empirical Rule Example 0 Above what number for 25 of the balances lie 0 1325 225 0 1375 is 2 standard deviations above the mean Empirical Rule Example 0 What percent of balances are between 1250 and 1400 0 Z score 0 1250 1325 25 3 o 1400 1325 25 3 0 What percent of balances are between sigma 3 and sigma 3 O 99700 Example 0 Mean 07 0 Standard Deviation 01 0 Middle 95 of students who drink 5 beers 2 standard deviations o 07 201 o 07 02 0 Between 05 and 09 o What of students who drink 5 beers have BAC above 08 0 One standard deviation above the mean see from graph 0 080701 1 zscore 0 how much left over from picture 100 84 16 left over 0 Taking the pieces and addingsubtracting to get what we want Percentiles The Cth percentile of a distribution is a value such that c percent of the observations lie below it and the rest lie above it 0 Not actually a percent Calculating Percentiles 0 Calculate the standardized score zscore 0 Use table B the Standard Normal table to find the percentile for the closest zscore If you are looking for the of observations BELOW your zscore your answer is the percentile which is the value from the table More about Percentiles 0 Negative Zscore below mean percentile lt 50 Zscore 0 percentile 50 0 Positive Zscore above mean percentile gt 50 Strategy for Normal Problems 0 Forward or Backward 0 Looking for percentage forward already know datax 0 Looking for observed values backward know Forward Normal 0 What is the 0 Know observed value 0 Use table standard score Z percentile 0 Convert to Z at start Backward Normal 0 What is the observed value 0 Know 0 Use table percentile standard score Z Example 0 What percentage of accounts will have less than 1270 in them 1270132525 22 zscore 0 Match up to the table 139 Forward Examples Example 0 What of accounts will have gt 1380 o Forwards problem 0 Have x and want Mue 1325sigma 25 1380132525 22 0 percentile 22 associated with 9861 from chart 0 ABOVE 100 9861 Example 0 What of accounts will have lt 1380 0 Normal is symmetric meanmedian o 1325132525 0 50 Example 0 What of accounts will have lt 10 0 Forwards problem x 10 want o 10132525 526 Percentile about 0 0 There is hardly any area under the curve this far out in the left tail Backwards Examples 0 Know percentile and looking for the Zscore to calculate observed value x 0 Look at the chart Example 0 What is the account balance that marks the top of the bottom 20 o What is the x 0 20th percentile 2119 08 standard score 132508x25 Examples 0 Top 15 0 Standard score 10 from chart 13251025 1350 Example 0 IQ score being below a score of 85 Forward lt 8510015 1 0 Look at tablechart 187 Example 0 Sleep 0 Mue 7quotsigmaquot 1 1 of students sleep lt 4hrs 0 471 3 Zscore 0 Look at the chart for 13 2 What sleep more than 75hrs o 7571 5 0 Look at chart 1006915 3085 3 If a student falls in the lowest 2 of the distribution heshe would sleep less than hours 0 7 20 1 49 4 What sleep between 6582 hours 0 do both zscore and subtract Example 0 Mean 73 0 Standard deviation 12 between 40 and 81 o 407312 28 26 o 817312 7 758 0 Look at table for percentile o 26 75800 between 49 and 100 o 497312 2 o 1007312 225 0 Look at table for percentile 22615 126 PM 22615 126 PM

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