Suppose the grades of a certain exam are normally distributed with a mean of 72 and a standard deviation of 8. The instructor is going to award bonus points to all students whose grade is in the top 5%. What is the minimum grade a student needs to have to qualify for the bonus points

The minimum grade a student needs to have to qualify for the bonus points is of 85.16.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of 72 and a standard deviation of 8.

This means that

What is the minimum grade a student needs to have to qualify for the bonus points?

The 100 - 5 = 95th percentile, which is X when Z has a p-value of 0.95, so X when Z = 1.645.

The minimum grade a student needs to have to qualify for the bonus points is of 85.16.

step-by-step explanation:

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