IQ scores as measured by both the Stanford-Binet intelligence test and the Wechsler intelligence test have a mean of 100. The standard deviation for the Stanford-Binet test is 16, while that for the Wechsler test is 14. For which test do a smaller percentage of test-takers score less than 80 ?
A)Wechsler
B) Stanford-Binet
C) Percentages are equal

Question

IQ scores as measured by both the Stanford-Binet intelligence test and the Wechsler intelligence test have a mean of 100. The standard deviation for the Stanford-Binet test is 16, while that for the Wechsler test is 14. For which test do a smaller percentage of test-takers score less than 80  ?
A)Wechsler
B) Stanford-Binet
C) Percentages are equal

Quizplus · Accepted Answer

To find out which test has a smaller percentage of test-takers who score less than 80, we need to convert this score to a standard score (or z-score) for each test using the formula z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation.

For the Stanford-Binet test, z = (80 - 100) / 16 = -1.25
For the Wechsler test, z = (80 - 100) / 14 = -1.43

We can then use a standard normal distribution table (or calculator) to find the percentage of test-takers who score less than these z-scores (which represent standardized scores of 80 on each test).

Using the table or calculator, we find that the percentage of test-takers who score less than -1.25 is 10.07% for the Stanford-Binet test, and the percentage who score less than -1.43 is 7.67% for the Wechsler test.

Therefore, a smaller percentage of test-takers score less than 80 on the Wechsler test, making A the best choice.

IQ Scores as Measured by Both the Stanford-Binet Intelligence Test