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

Since the area to the right of \(x\) is \(0.65\), the area to the left of \(x\) is \(1 - 0.65=0.35\). Looking up the \(z\) - score in the standard normal distribution table (or using a calculator with a normal - distribution function), the \(z\) - score corresponding to an area of \(0.35\) is approximately \(z=- 0.39\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 100\) (mean) and \(\sigma = 15\) (standard deviation).
Substitute \(z=-0.39\), \(\mu = 100\), and \(\sigma = 15\) into the formula:
\(-0.39=\frac{x - 100}{15}\)
Multiply both sides by \(15\):
\(x-100=-0.39\times15\)
\(x - 100=-5.85\)
Add \(100\) to both sides:
\(x=100-5.85\)

Answer:

\(x = 94\)