If test scores are approximately normally distributed with mean 82 and standard deviation 8, what score would correspond to the 80th percentile

A score of 88.72 corresponds to the 80th percentile.

Step-by-step explanation:

Problems of normal distributions can be 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.

Mean 82 and standard deviation 8

This means that

What score would correspond to the 80th percentile

This is X when Z has a pvalue of 0.8, so X when Z = 0.84.

A score of 88.72 corresponds to the 80th percentile.

72 is the answer to this problem

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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