Intelligence quotas on two different tests are normally distributed. test a has a mean of 100 and a standard deviation of 13. test b has a mean of 100 and a standard deviation of 18. usez-scores to determine which person has the higher iq: an individual who scores 123 on test a or an individual who scores 121 on test b. which individual has the higher iq?

The individual who scores 123 on test A has a higher zscore, so he has the higher IQ.

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:

The individual with the higher IQ is the one with the higher z-score. So

Test A has a mean of 100 and a standard deviation of 13. An individual who scores 123 on Test A.

So

Test B has a mean of 100 and a standard deviation of 18. An individual who scores 121 on Test B.

So

The individual who scores 123 on test A has a higher zscore, so he has the higher IQ.