Question

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?

Answer 1

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.