A student scored two standard deviations below the mean for children in her grade (7th grade) in Reading and received a standard score of 115 in Mathematics where the mean is 100 with a standard deviation of 15 points for the test that follows the bell curve. How can we…
A reading score that is two standard deviation below the mean implies that the student belongs to the bottom 3% of the grade sevens, implying that close to 97% of the grade sevens are ahead of her in the test. In what may be clearer terms, this means that if there are only 20 grade seven students, the student who scored two standard deviations from the mean in Reading means that she is about only as good as the slowest academic performer in 20 students. Make the students 100 instead of 20, a two standard deviation score below the mean score in reading means that she is about as good as third slowest academic performer in a reading if there only 100 grade seven students. These discussions are not very accurate, however, and were meant to impress important mental images of the situation.
Table 1 refers to select portions of the normal curve. A test score that is two standard deviation from the mean imply a z-Score of -2.0 that is associated with -2.00. The numeral -2.00 follows through the intersection of the row of -2.0 in the z column and the column associated with .00 of the table. In turn, following protocols followed for the table of the normal curve, the numerals mentioned earlier are associated with the value of 0.0228 that gives area under the normal curve. The area of normal curve 0.0228 is associated with the probability associated with the lowest scorer with the score associated with two standard deviations below the mean. This means that more precisely the student we are discussing belong to bottom 2.28% of the grade sevens, following the association of 0.0228 with 2.28%.
Meanwhile, a score of 115 given of 100 and standard deviation of 15 imply a z value of 1.15 following standard transformation formation protocols. In turn, the z-score of 1.15 is associated with the area 0.8749 under the normal curve based on Table 1. This means that the student we are ...
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