assume that adults have iq scores that are normally distributed with a mean of μ = 105 and a standard…

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.)

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.)

Answer

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:

$0.8413$