Question

assume that adults have iq scores that are normally distributed with a mean of 104 and a standard deviation of 20. find the probability that a randomly selected adult has an iq greater than 138. (hint: draw a graph.) the probability that a randomly selected adult from this group has an iq greater than 138 is . (round 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 $x = 138$, $\mu=104$, and $\sigma = 20$. So, $z=\frac{138 - 104}{20}=\frac{34}{20}=1.7$.

Step2: Find the probability associated with the z - score

We want $P(X>138)$, which is equivalent to $P(Z > 1.7)$ in the standard normal distribution. Since the total area under the standard - normal curve is 1, and $P(Z>z)=1 - P(Z\leq z)$. Looking up the value of $P(Z\leq1.7)$ in the standard - normal table, we find that $P(Z\leq1.7)=0.9554$. Then $P(Z > 1.7)=1 - 0.9554 = 0.0446$.

Answer:

0.0446