Step 1 :Given that adults have IQ scores that are normally distributed with a mean (\(\mu\)) of 105 and a standard deviation (\(\sigma\)) of 15.
Step 2 :We are asked to find the probability that a randomly selected adult has an IQ less than 126.
Step 3 :This is a problem of normal distribution. In a normal distribution, the probability that a value is less than a certain value can be found by calculating the z-score of that value and then looking up the probability associated with that z-score in a standard normal distribution table.
Step 4 :The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation. The formula for calculating the z-score (\(Z\)) is \(Z = \frac{X - \mu}{\sigma}\), where \(X\) is the value.
Step 5 :Substituting the given values into the formula, we get \(Z = \frac{126 - 105}{15} = 1.4\).
Step 6 :Looking up the z-score of 1.4 in a standard normal distribution table, we find that the probability associated with this z-score is approximately 0.9192.
Step 7 :Thus, the probability that a randomly selected adult has an IQ less than 126 is approximately \(\boxed{0.9192}\).