Questions: 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.)

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.)

Transcript text: 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 $\square$ . (Round to the nearest whole number as needed.)

Solution

Solution Steps

Step 1: Understand the Problem

The problem requires finding the indicated IQ score from a normal distribution graph. The IQ scores are normally distributed with a mean (μ) of 100 and a standard deviation (σ) of 15. The graph shows a shaded area representing a probability of 0.4207.

Step 2: Identify the Z-Score

The shaded area to the right of the indicated IQ score represents the probability. To find the corresponding Z-score, we need to look up the cumulative probability (1 - 0.4207 = 0.5793) in the Z-table.

Step 3: Look Up the Z-Score

Using the Z-table, we find that a cumulative probability of 0.5793 corresponds to a Z-score of approximately 0.20.

Step 4: Calculate the IQ Score

Use the Z-score formula to find the IQ score: \[ Z = \frac{X - \mu}{\sigma} \] \[ 0.20 = \frac{X - 100}{15} \] \[ X - 100 = 0.20 \times 15 \] \[ X - 100 = 3 \] \[ X = 103 \]