Final answer:
After calculating the z-score corresponding to the given area and applying it to the IQ distribution formula, the nearest IQ score to the calculated value of 103.75 is 105.4, which is option B.
Step-by-step explanation:
To find the IQ score when the area to the right of x is 0.4, and knowing that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, we use the Z-table. Since tables typically give the area to the left, we need to subtract 0.4 from 1 to get the area to the left, which is 0.6.
Looking up the area 0.6 on the Z-table, we find the corresponding z-score is approximately 0.25. We can then use the z-score formula:
Z = (X - μ) / σ
Rearranging to solve for X:
X = Z * σ + μ
X = 0.25 * 15 + 100
X = 3.75 + 100
X = 103.75
Looking at the options provided, the nearest value to 103.75 is B. 105.4, which is the correct option answer in the final answer.