122k views
3 votes
What percentage of IQ scores would you expect to find in a normal distribution (Mean=100; sd=15) between the scores of 85 and 145?

a) 68%
b) 95%
c) 99%
d) 34%

User Frooyo
by
8.5k points

1 Answer

5 votes

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%.

User Pat Notz
by
8.5k points