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23.06.2021 •
Mathematics
A person must score in the upper of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of and a standard deviation of , what score must a person have to qualify for Mensa (to whole number)
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Ответ:
The person must score at least
, in which Z has a p-value of
, considering p the upper percentage the person must score,
is the mean IQ score for the population and
is the standard deviation.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
In this question:
Mean
, standard deviation ![\sigma](/tpl/images/1381/8036/42440.png)
What score must a person have to qualify for Mensa?
Score of at least X, given by:
In which Z has a p-value of
, considering p the upper percentage the person must score.
Ответ:
5. 2898.59.
7. 42%