Question

The most common intelligence quotient (IQ) scale is normally distributed with mean 100 and standard deviation 15. Many school districts across the country seek to identify "Gifted and Talented" children for special enrichment programs. Typically, these children must have IQ scores in the top 5%. What is the minimum score to qualify a child for these programs?

Answer 1

125

Explanation:

Since we know that the IQ scale is normally distributed with mean = 100 and standard deviation 15. We can simply get z-score. A z-score of 1.645 which is a midpoint of z = 1.64 with 0.9495 and z = 1.65 with 0.9505 below that z-score will have 95% of all students below that value, therefore 5% above it will be (1.645)(15) + 100 = 124.675,the score is roughly to 125