Assume that adults have 10 scores that are normally distributed with a mean of =105 and a standard deviation of =15. Find the probability that a randomly selected adult has an IQ less than 126 .
The probability that a randomly selected adult has an IQ less than 126 is
(Type an integer or decimal rourided to four decimal places as needed)

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 \(\boxed{0.9192}\).