The scores of adults on an IQ test are approximately Normal with mean 100 and standard deviation 15. The organization MENSA, which calls itself 'the high IQ society', requires an IQ score of 130 or higher for membership. About what percent of adults would qualify for membershipA. 67%
B. 2.5%
C. 95%
D. 5%
E. None of the above.

B. 2.5%

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:

The organization MENSA, which calls itself 'the high IQ society', requires an IQ score of 130 or higher for membership. About what percent of adults would qualify for membership

This percentage is 1 subtracted by the pvalue of Z when X = 130. So

has a pvalue of 0.9772

1 - 0.9772 = 0.0228.

2.28% is close to 2.5%, so the correct answer is:

B. 2.5%