IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Mensa is an international society that has one - and only one - qualification for membership: a score in the top 2% of the population on an IQ test. (a) What IQ score should one have in order to be eligible for Mensa? (b) In a typical region of 145,000 people, how many are eligible for Mensa

a) In order to be eligible for Mensa, a person must have an IQ score of at least 130.81.

b) 2900 people are elegible for Mensa.

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:

(a) What IQ score should one have in order to be eligible for Mensa?

Scores in at least the 98th percentile, so scores of at least X when Z has a pvalue of 0.98. So at least X when Z = 2.054.

In order to be eligible for Mensa, a person must have an IQ score of at least 130.81.

(b) In a typical region of 145,000 people, how many are eligible for Mensa

Only 2% are elegible. So

0.02*145000 = 2900

2900 people are elegible for Mensa.

the answer is d

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