Question

The mean IQ score for 1,500 students is 100, with a standard deviation of
15. Assuming a normal distribution of scores, how many students have an
IQ between 85 and 115?

Answer 1

This is what I know. The bell shaped distribution is cut in half, 50% one side and 50% on the other. 1 standard deviation is 34% of the observed values. 34% is half of the distribution so 100% is 68%. 68% of 1500 students is 1020

Answer 2

It would be better if you had put your initial reasoning in a similar form to this:

In all Normal distributions approximately 68% of the data points lie within the range of plus and minus one standard deviation of the mean.

Answer 3

you can use empirical rule or z table.