Question

previous question question 17 of 20 next question iq scores are known to be normally distributed. the mean iq score is 100 and the standard deviation is 15. the top 25% of the population (ranked by iq score) have iq's above what value?

Answer 1

The top 25% of the population, based on IQ scores, have scores above approximately 110.

Step-by-step explanation:

The student is seeking the IQ score that marks the top 25% of the population, given the distribution is normal with a mean of 100 and a standard deviation of 15. To find this value, we look at the corresponding percentile in a standard normal distribution

A score in the top 25% of the population corresponds to the 75th percentile. We can find this value using a Z-table or standard normal distribution calculator. The Z-score for the 75th percentile is approximately 0.6745. This means that the IQ score we are searching for is 0.6745 standard deviations above the mean.

Let's calculate the IQ score using the Z-score formula:

1. Z = (X - mean) / standard deviation
2. 0.6745 = (X - 100) / 15
3. X = 0.6745 * 15 + 100
4. X ≈ 110.12

Therefore, the top 25% of the population, ranked by IQ score, have IQ scores above approximately 110.