In a recent year, scores on a standardized test for highschool students with a 3

Question

In a recent year, scores on a standardized test for highschool students with a 3.50 to 4.00 grade point average werenormally distributed, with a mean of 37.1 and a standard deviationof 1.9. A student with a 3.50 to 4.00 gpa who took the standardizedtest is randomly selected. A) The probabilty of a student scoring less than 33 iswhat? B) The probability of the student scoring between 33.7 and40.5 is what? C) The probability of a student scoring more than 38.8 iswhat? In a recent year, scores on a standardized test for highschool students with a 3.50 to 4.00 grade point average werenormally distributed, with a mean of 37.1 and a standard deviationof 1.9. A student with a 3.50 to 4.00 gpa who took the standardizedtest is randomly selected. A) The probabilty of a student scoring less than 33 iswhat? B) The probability of the student scoring between 33.7 and40.5 is what? C) The probability of a student scoring more than 38.8 iswhat?

Explanation / Answer

a)The z-score for a score of 33 is (33-37.1)/1.9=-2.1579.Using a z-table or software you can calclate the probability ofseeing that z-score or lower (using software I get .01547, or about1.55% _______________________________________________________________________________________ b)z-score for 33.7 is (33.7-37.1)/1.9=-1.7895 and z-score for40.5 is (40.5-37.1)/1.9=1.7895. Using a z-table or software,calculate the probability of oberving this range of z-scores (withtable, subtract area below -1.7895 from 1.7895 to get area betweenthe two). I get .9265 or about 92.65% _______________________________________________________________________________________ _______________________________________________________________________________________ c)z-score for 38.8 is (38.8-37.1)/1.9=.89473. Using z-table rosoftware, calculate the probability of observing this z-score orhigher. I get .18546, or about 18.55%

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