A paper "Meaning Socio-Cultural Factors Involved In Education" claims that 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…
A test score that is two standard deviation from the mean implies 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. 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 implies 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. The student we are discussing belong to the bottom 87.49% of the grade sevens. Described in another way, only 12.51% of the students of grade seven are ahead of our student. We can also say that our student belongs close to the top 13% of the grade sevens. If there are only 100-grade sevens, our student closely belongs to the best 13 students of the grade sevens. We can say that our student is one of the “laggards” with regard to performance in reading but one of the best with regard to performance in mathematics. ...
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