Final answer:
The percentage of IQ scores between 85 and 145 in a normal distribution with a mean of 100 and an sd of 15 is a bit more than 95%. The correct answer is b) 95%.
Step-by-step explanation:
The question asks for the percentage of IQ scores within a normal distribution with a mean of 100 and a standard deviation of 15 between the scores of 85 and 145.
In a normal distribution, approximately 68% of data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.
Since 85 is one standard deviation below the mean (100 - 15) and 145 is three standard deviations above the mean (100 + 3*15), the percentage of scores we're looking for would span from one standard deviation below the mean to three standard deviations above it, hence encompassing 68% + 27% (half of 95% minus 68%) and a bit of the remaining 4.7% (the half beyond two standard deviations above the mean).
As such, the answer should therefore include a bit more than 95%.