The middle 50% of IQs fall between what two values?

Question

IQ is normally distributed with a mean of 100 and a standard deviation of 15. The middle 50% of IQs fall between what two values?

Answer 1

Ok, so the middle 50% is the IQR. So we are essentially looking at the 25 percentile and the 75 percentile. So now we just have to look on the Z table to see which Z score is greater than or equal to the lowest 25 percent of Z scores. Same with the 75 percentile. So we know:

For the .25 area, Z=-0.674

For the .75 area, Z = 0.674.

So we just need to find y. So, now we have 0.674=x-100/15

15*.674=x-100

-10.11=x-100

100-10.11=x

89.89=x

We also need to plug in:

10.11=x-100

110.11

.674=x-100/15

So the middle 50% of scores fall in between 89.89 and 110.11