Answer:
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.