find the indicated iq score. the graph to the right depicts iq scores of adults, and those scores are…
find the indicated iq score. 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. click to view page 1 of the table. click to view page 2 of the table. the indicated iq score, x, is (round to the nearest whole number as needed.)
Answer
Explanation:
Step1: Use z - score formula
The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We need to find the z - score corresponding to the area under the curve. The area to the left of $x$ is $0.8$.
Step2: Look up z - score in the standard normal table
Looking up the area of $0.8$ in the standard - normal (z - score) table, the z - score $z\approx0.84$.
Step3: Solve for $x$
We know that $\mu = 100$, $\sigma=15$, and $z = 0.84$. Substitute into the z - score formula $z=\frac{x - \mu}{\sigma}$ and solve for $x$. Rearranging the formula gives $x=\mu+z\sigma$. Substitute the values: $x = 100+0.84\times15$. $x=100 + 12.6=112.6$.
Answer:
113