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Answer:
Grades between 62 and 64 result in a D grade.
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:
Find the numerical limits for a D grade.
D: Scores below the top 84% and above the bottom 10%
So below the 100-84 = 16th percentile and above the 10th percentile.
16th percentile:
This is the value of X when Z has a pvalue of 0.16. So X when Z = -0.995.
10th percentile:
This is the value of X when Z has a pvalue of 0.1. So X when Z = -1.28.
Grades between 62 and 64 result in a D grade.