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Normal Distribution using the TI-83 Graphing Calculator

Normal Distribution using the TI-83 Graphing Calculator. To access the TI-83 functions for Normal Distributions Press 2 nd and VARS. normalpdf ( height of the curve. The TI-83 provides three functions for Normal Distribution:. normalcdf ( area under the curve.

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Normal Distribution using the TI-83 Graphing Calculator

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  1. Normal Distributionusing the TI-83 Graphing Calculator

  2. To access the TI-83 functions for Normal DistributionsPress 2ndand VARS

  3. normalpdf( height of the curve The TI-83 provides three functions for Normal Distribution: normalcdf( area under the curve invNorm( score associated with the given area

  4. Area or Probability Area under the Curvenormalcdf(low, high, mean, stdev)Returns the area under the curve (aka: probability, relative frequency)between the low and high scores.

  5. Between 2 scores • This would return the area under a normal curve between 112 and 122 for a distribution that has a mean of 100 and a standard deviation of 15.

  6. Below a score: <112 • This would return the area under a normal curve below 112 (to the left) • Assumes there is no data below -9999.

  7. z-scores A standard or z-score measures the distance between each item and the mean in terms of the number of standard deviations. The z-score based on a raw score of 112 for a distribution that has a mean of 100 and a standard deviation of 15would be: = 0.8

  8. Between 2 z-scores The normalcdf function defaults to a mean of zero and a standard deviation of one: these are the parameters for the standard normal distribution.

  9. Between 2 z-scores This would return the area under a standard normal curve between the z-scores of -1.5 and 2.

  10. Below a z-score Another way to find the cumulative area for scores below 112, would be to first convert to a z-score: = 0.8 Find the area in the standard normal distribution. Since there is very little data more than 3.5 standard deviations below the mean, use any z-score below -3.5 as the low bound: Normalcdf(-5,0.8) Would return the area below z=0.8, which is The area below the raw score of 112.

  11. Above a z-score To find the area ABOVE 112, you could subtract the area below 112 from 1. The total area under the curve = 1. (Total probability = 100%) OR use any z-score ABOVE 3.5 as the upper bound: Normalcdf(0.8, 5) Would return the area ABOVE z=0.8, which is The area Above the raw score of 112.

  12. Inverse: invNorm() The Inverse Function While normalcdf( L,H,,s) returns an area or probability given a Low and High bound, the inverse function: invNorm(p,,s) returns a High bound when given a probability. Like normalcdf( L,H) , invNorm(p) uses a default mean of zero and standard deviation of one: for the standard normal distribution.

  13. invNorm() This invNorm() function would return the score associated with the 90th percentile. 90% of the data would fall below this score and 90% of the area under the curve would be to the left of this Raw score. Note: When you want the Raw score, enter values for mean and standard deviation. The default is to use the standard normal distribution – and to return a z-score

  14. invNorm() This invNorm(.25) function would return the z-score associated with the 25th percentile. 25% of the data would fall below this score and 25% of the area under the curve would be to the left of this z-score. Note that 75% of the data would fall ABOVE this score and 75% of the area under the curve would be to the RIGHT of this z-score.

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