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 z - score

Since the area to the left of \(x\) is \(0.3446\), we look up this value in the standard normal distribution table. The corresponding \(z\) - score is approximately \(z=-0.40\)

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 100\), \(\sigma=15\) and \(z=-0.40\)
Substitute the values into the formula: \(-0.40=\frac{x - 100}{15}\)

Step3: Solve for \(x\)

Multiply both sides of the equation by \(15\): \(-0.40\times15=x - 100\)
\(-6=x - 100\)
Add \(100\) to both sides: \(x=100-6\)

Answer:

\(94\)