The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a person would score between 85 and 115?
A) 0.3413
B) 0.6826
C) 1.00
D) Very likely

Question

Quizplus · Accepted Answer

To find the probability of a person scoring between 85 and 115, we need to calculate the area under the normal distribution curve between these two scores.

First, we find the z-scores for both values:

z-score for 85 = (85 - 100) / 15 = -1

z-score for 115 = (115 - 100) / 15 = 1

Using a z-table or calculator, we can find the area under the normal distribution curve between these two z-scores.

Area between z = -1 and z = 1 = 0.6826

Therefore, the probability that a person would score between 85 and 115 is 0.6826 or 68.26%.

The Intelligence Quotient (IQ) Test Scores Are Normally Distributed with a Mean