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 \(0.35\) in the standard normal distribution table (z - table), the corresponding \(z\) - score 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:
\(-0.39=\frac{x - 100}{15}\)

Step3: Solve for \(x\)

Multiply both sides of the equation by \(15\): \(-0.39\times15=x - 100\)
\(-5.85=x - 100\)
Add \(100\) to both sides: \(x=100-5.85\)
\(x = 94.15\approx94\)

Answer:

\(94\)