Question

assume that adults have iq scores that are normally distributed with a mean of μ = 100 and a standard deviation σ = 20. find the probability that a randomly selected adult has an iq less than 120. 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 120 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 $x = 120$, $\mu=100$, and $\sigma = 20$.
$z=\frac{120 - 100}{20}=\frac{20}{20}=1$

Step2: Find the probability from the standard normal table

We want to find $P(X<120)$, which is equivalent to $P(Z < 1)$ in the standard - normal distribution. Looking up the value of $P(Z < 1)$ in the standard normal table, we get $0.8413$.

Answer:

$0.8413$