 # Math Statistics Essay

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In this mathematical circumstance, it is appropriate to use the Normal Model with this data distribution because of how roughly symmetric and unimodal. The summary statistics for the OB Math SAT scores are as follow: the number of values is 287, the mean of the data is 553.62369, the standard deviation is of approximately 65.984512, the median of the data is 540, the range of the data is 390, the minimum value is 360, the maximum value is 750, the first quartile of the data is 510, and the second quartile of the data is 590. To calculate the percent of students that had an SAT math score higher than 560, I used the z-score formula which is z-score= raw score- mean/ standard deviation and plugged the values for each variable. After…show more content…
After solving for the variable and then plugged in the values and I got raw score= 0.8416 (65.984512) + 553.62369 which gave us a raw score of 609 rounded to the nearest integer. To be in the top 5% of the class a student would need to have a SAT score of around 662. I have come to that conclusion by simply converting 5 into a decimal number (5/100) and then plugging that decimal number (0.05) into invNorm in the calculator which gave us invNorm (0.05, 0, 1) = -1.6448. I then changed the number into a positive value to calculate the top 5%, and then plugged it into our raw score formula that we solved earlier and got raw score= 1.6448 (65.984512) + 553.62369 which gave us a raw score of 662 rounded to the nearest integer. To calculate the z-score at the 25th percentile of the model I converted 25 into a decimal number (25/100) and then plugged that decimal number (0.25) into invNorm in the calculator which gave us invNorm (0.25, 0, 1) = -0.6744. Then to calculate the raw score at the 25th percentile I plugged the z-score -0.6744 into the raw score formula we solved earlier and got raw score= -0.6744 (65.984512) + 553.62369 which gave us a raw data value of 509 rounded to the nearest integer. The z-score and raw data value at 75th percentile of the model is 0.6744 and 598. To calculate the z-score at the 75th percentile of the model I converted 75 into a decimal (75/100) and then plugged that decimal number (0.75) into