In 2012, New York Yankees baseball players earned an average salary of $6,186,321, with a standard deviation of $7,938,987. Assuming that these data are normally distributed, what was the salary of a player in the 53rd percentile?

The salary of a player in the 53rd percentile was $6,781,745.

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

Assuming that these data are normally distributed, what was the salary of a player in the 53rd percentile?

This is the value of X when Z has a pvalue of 0.53. So X when Z = 0.075.

So

The salary of a player in the 53rd percentile was $6,781,745.

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