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 $x = 79$, $\mu=100$, and $\sigma = 15$. So, $z=\frac{79 - 100}{15}=\frac{- 21}{15}=-1.4$.

Step2: Find the area from the z - table

We want to find $P(X<79)$, which is equivalent to $P(Z < - 1.4)$ using the standard normal distribution. Looking up the value of $-1.4$ in the standard normal (z -) table, we find that the area to the left of $z=-1.4$ is $0.0808$.

Answer:

$0.0808$