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Final numeric grades in a certain course are normally distributed with a mean of 72.3 and a standard deviation of 6.4. The professor curves the grades so that the top 8% of students will receive an A. What is the minumum numeric grade you have to earn to obtain an A?

User Unjuken
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1 Answer

5 votes

Answer:

The minumum numeric grade you have to earn to obtain an A is 81.29.

Explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean
\mu and standard deviation
\sigma, the zscore of a measure X is given by:


Z = (X - \mu)/(\sigma)

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:


\mu = 72.3, \sigma = 6.4

The professor curves the grades so that the top 8% of students will receive an A. What is the minumum numeric grade you have to earn to obtain an A?

The minimum numeric value is the value of X when Z has a pvalue of 1-0.08 = 0.92. So it is X when Z = 1.405.

So


Z = (X - \mu)/(\sigma)


1.405 = (X - 72.3)/(6.4)


X - 72.3 = 1.405*6.4


X = 81.29

The minumum numeric grade you have to earn to obtain an A is 81.29.

User Jens Peter
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