Answer:
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:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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](https://tex.z-dn.net/?f=%5Csigma)
What score must a person have to qualify for Mensa?
Score of at least X, given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![X - \mu = Z\sigma](https://tex.z-dn.net/?f=X%20-%20%5Cmu%20%3D%20Z%5Csigma)
![X = \mu + Z\sigma](https://tex.z-dn.net/?f=X%20%3D%20%5Cmu%20%2B%20Z%5Csigma)
In which Z has a p-value of
, considering p the upper percentage the person must score.