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Answer:
The numerical limits for a B grade is between 81 and 89.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
B: Scores below the top 13% and above the bottom 56%
Below the top 13%:
Below the 100-13 = 87th percentile. So below the value of X when Z has a pvalue of 0.87. So below X when Z = 1.127. So
Above the bottom 56:
Above the 56th percentile, so above the value of X when Z has a pvalue of 0.56. So above X when Z = 0.15. So
The numerical limits for a B grade is between 81 and 89.