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 136. 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 136 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 $x = 136$, $\mu=100$, and $\sigma = 20$.
$z=\frac{136 - 100}{20}=\frac{36}{20}=1.8$

Step2: Find the probability using the standard normal distribution table

We want to find $P(X\lt136)$, which is equivalent to $P(Z\lt1.8)$ in the standard - normal distribution. Looking up the value of $z = 1.8$ in the standard normal distribution table, we get $P(Z\lt1.8)=0.9641$.

Answer:

$0.9641$