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: Find the z-score

The area to the right of x is 0.2525. We want to find the z-score corresponding to the area to the left of x. The area to the left of x is 1 - 0.2525 = 0.7475. Using a z-table or calculator, we find that the z-score corresponding to a cumulative probability of 0.7475 is approximately 0.67.

Step 2: Calculate the IQ score

We are given that the mean IQ score is 100 and the standard deviation is 15. We can use the formula:

x = μ + zσ

Where x is the IQ score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we get:

x = 100 + (0.67)(15) x = 100 + 10.05 x ≈ 110.05

Step 3: Round to the nearest whole number

Rounding to the nearest whole number, we get 110.