find the area of the shaded region. the graph to the right depicts iq scores of adults, and those scores are…

find the area of the shaded region. the graph to the right depicts iq scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. the area of the shaded region is . (round to four decimal places as needed.)

find the area of the shaded region. the graph to the right depicts iq scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. the area of the shaded region is . (round to four decimal places as needed.)

Answer

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 91$, $\mu=100$, and $\sigma = 15$. So $z=\frac{91 - 100}{15}=\frac{-9}{15}=- 0.6$.

Step2: Find the area to the right of the z - score

We want to find $P(X>91)$, which is equivalent to $P(Z>-0.6)$ 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 $P(Z\leq - 0.6)$ in the standard normal table, we find that $P(Z\leq - 0.6)=0.2743$. Then $P(Z>-0.6)=1 - 0.2743 = 0.7257$.

Answer:

$0.7257$