# Find the probability that a randomly selected adult has an IQ greater than 131.5assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15.

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justaguide | Certified Educator

The IQ of adults is normally distributed with a mean of 100 and a standard deviation of 15. To determine the probability that that an adult has an IQ greater than 131.5, find the z-score of 131.5

The z-score for a value x is given by `(x - mu)/sigma`

Here `mu = 100` and `sigma = 15` .

The z-score is `(131.5 - 100)/15 = 2.1`

Use a normal distribution table to find the corresponding area for this z-score. The value is 0.9821. 98.21% of values lie below 131.5. The probability that an adult has an IQ greater than 131.5 is 1 - 0.9821 = 0.0179

**There is 1.79% probability that the IQ of a randomly chosen adult is greater than 131.5**