Suppose the scores on an IQ test are approximately normally distributed with a mean of 100 and a standard deviation of 10. What is the probability that a randomly selected person scores above 125 on the IQ test

0.62% probability that a randomly selected person scores above 125 on the IQ test

Step-by-step explanation:

Problems of normally distributed samples 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.

In this problem, we have that:

What is the probability that a randomly selected person scores above 125 on the IQ test

This is 1 subtracted by the pvalue of Z when X = 125. So

has a pvalue of 0.9938

1 - 0.9938 = 0.0062

0.62% probability that a randomly selected person scores above 125 on the IQ test