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A makeup test is given and the average (μX) score out of 100 was 85.0, with...

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Statistics

A makeup test is given and the average (μX) score out of 100 was85.0, with a SD (σX) of 3.0. Assuming a normal distribution, findthe dividing line (test scores) between the A's, B's, C's, D's, andE's. This time the highest 6% will be the A's, the next 16% B's,the next 26% C's, the next 36% D's.

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Given Mean X 85Standard deviation X 3Assuming a normal distribution find the dividing line testscores between the As Bs Cs Ds and Es This time thehighest 6 will be the As the next 16 Bs the next 26 Cs thenext 36 DsAs from BsWe will find the test score between As and BsSince the highest 6 are be the As then we know that other 94are less than As We can determine the zscore from the ztableusing the pvalue which is the area to the left of zscore and thenfind the respective test scoresHere pvalue is 094 which is the area to the left ofzscoreI have attached the ztables at the end We will calculate thezscores using pvalues from the respective tableIn the positve ztable the area nearest to 094 is 093943 whichis for a zscore of 155The exact zscore for a pvalue of 094 is 15548We know thatZscore X X X15548 X 85 3X 85 46644X 896644X 89664 rounded to three dcimal placesSo a test score of 89664 differentiate the As from BsBs from CsWe will find the test score between Bs and CsSince the highest 6 are be the As the next 16 are Bs thenwe know that other 22 are less than Bs We can determine thezscore from the ztable using the pvalue which is the area to theleft of zscore and then find the respective test scoresHere pvalue is 078 which is the area to the left ofzscoreI have attached the ztables at the end We will calculate thezscores using pvalues from the respective tableIn the positve ztable the area nearest to 078 is 07735 whichis for a zscore of 077The exact zscore for a pvalue of 077219We know thatZscore X X X07722 X 85 3X 85 23166X 873166X 87317 rounded to    See Answer
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