Question

When the Stanford-Binet IQ test came into use in 1932, it was adjusted so that scores for each age group of children followed roughly the Normal distribution with mean 100 and standard deviation 15. The test is readjusted from time to time to keep the mean at 100. If present-day American children took the 1932 Stanford-Binet test, their mean score would be about 120. The reasons for the increase in IQ over time are not known but probably include better childhood nutrition and more experience in taking tests.

(a) IQ scores above 130 are often called "very superior." What percentage of children had very superior scores in 1932? (Enter your answer rounded to two decimal places.)
Percentage of children with very superior scores in 1932:...............%
(b) If present-day children took the 1932 test, what percentage would have very superior scores? Assume that the standard deviation of 15 does not change. (Enter your answer rounded to two decimal places.)
Percentage of present-day children with very superior scores:..................%

Answer 1

In 1932, approximately 2.28% of children had very superior scores on the Stanford-Binet IQ test. If present-day children took the 1932 test, approximately 2.28% of them would also have very superior scores.

Step-by-step explanation:

In 1932, when the Stanford-Binet IQ test was first used, scores were adjusted to follow a normal distribution with a mean of 100 and a standard deviation of 15. To find the percentage of children with very superior scores (IQ > 130) in 1932, we need to calculate the area under the normal curve to the right of IQ = 130.

Using a z-score table or a calculator, we find that the z-score corresponding to IQ = 130 is (130 - 100) / 15 = 2. The area to the right of this z-score is approximately 0.0228, or 2.28%. Therefore, in 1932, approximately 2.28% of children had very superior scores.

If present-day American children took the 1932 test, we can assume that their scores would still follow the same normal distribution with a mean of 100 and a standard deviation of 15. To find the percentage of present-day children with very superior scores, we again calculate the area under the normal curve to the right of IQ = 130.

Using the same process as before, we find that the z-score is still 2. The area to the right of this z-score remains approximately 0.0228, or 2.28%. Therefore, if present-day children took the 1932 test, approximately 2.28% of them would have very superior scores.