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 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 z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 120$, $\mu=105$, and $\sigma = 15$. So $z=\frac{120 - 105}{15}=\frac{15}{15}=1$.

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 $P(Z < 1)=0.8413$.

Answer:

$0.8413$