Question

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.)

Explanation:

Step1: Find the z - score

We know that the area to the left of \(x\) is \(A = 0.85\). Looking up the \(z\) - score in the standard normal distribution table (the \(z\) - value for which \(P(Z\lt z)=0.85\)). The \(z\) - score corresponding to an area of \(0.85\) is approximately \(z = 1.04\) (from the standard normal table).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 100\) (mean), \(\sigma=15\) (standard deviation), and \(z = 1.04\).
We can solve for \(x\) by re - arranging the formula: \(x=\mu+z\sigma\).
Substitute the values: \(x = 100+(1.04\times15)\).
First, calculate \(1.04\times15=15.6\).
Then, \(x=100 + 15.6=115.6\).

Answer:

\(116\)