Question

assume that adults have iq scores that are normally distributed with a mean of μ = 105 and a standard deviation σ = 15. find the probability that a randomly selected adult has an iq less than 126. click to view page 1 of the table. click to view page 2 of the table. the probability that a randomly selected adult has an iq less than 126 is (type an integer or decimal rounded to four decimal places as needed.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 126$, $\mu=105$, and $\sigma = 15$.
$z=\frac{126 - 105}{15}=\frac{21}{15}=1.4$

Step2: Find the probability from the standard normal table

We want to find $P(X<126)$, which is equivalent to $P(Z < 1.4)$ in the standard - normal distribution. Looking up the value of $z = 1.4$ in the standard normal table, we get $P(Z<1.4)=0.9192$.

Answer:

$0.9192$