Canadian Health Information Management Association Practice Exam

In a normal distribution of IQ scores with a mean of 115 and a standard deviation of 10, what percentage will have IQs less than 105?

1. 50%.

2. 5%.

3. 2.5% greater than 135.

4. 2.5% greater than 125.

The correct answer is: 5%.

To determine the percentage of individuals with IQ scores less than 105 in a normally distributed set of IQ scores, we can utilize the properties of the normal distribution, specifically the mean and standard deviation provided. In this context, the mean IQ score is 115, and the standard deviation is 10. To understand how to calculate the percentage of scores below 105, the first step is to convert the score of 105 into a z-score. The z-score is a way to describe how many standard deviations a particular score is from the mean. The formula for calculating a z-score is: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \( X \) is the score (105 in this case), - \( \mu \) is the mean (115), and - \( \sigma \) is the standard deviation (10). Substituting the values into the formula: \[ z = \frac{(105 - 115)}{10} = \frac{-10}{10} = -1 \] A z-score of -1 indicates that a score of 105 is one standard deviation below the mean. In a standard normal distribution table or using a calculator that provides cumulative probabilities