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. the indicated iq score is. (round to the nearest whole number as needed.)

Explanation:

Step1: Find the cumulative area to the left of \(x\)

The area to the right of \(x\) is \(0.2119\). So the cumulative area to the left of \(x\) is \(1 - 0.2119=0.7881\)

Step2: Find the \(z\) - score corresponding to the cumulative area

Using the standard normal distribution table (or a calculator with a normal - distribution function, e.g., invNorm on a TI - 84), for a cumulative area of \(A = 0.7881\), the \(z\) - score \(z\) is such that \(P(Z<z)=0.7881\). Looking up in the standard normal table, \(z\approx0.8\)

Step3: Use the \(z\) - score formula to find \(x\)

The \(z\) - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 100\), \(\sigma=15\), and \(z = 0.8\)
Rearrange the formula for \(x\): \(x=\mu+z\sigma\)
Substitute the values: \(x = 100+0.8\times15\)

$$x=100 + 12$$

Answer:

\(112\)