Question #fb52f
1 Answer
A)
B)
C)
Explanation:
To answer these questions, we would have to know if the standard IQ test results fall into a normal distribution. There is some debate online about that (many say it's meant to be a normal distribution, while the actual results are more likely to diverge from a normal distribution in the "tails"), but for this problem I believe it is intended to be treated that way.
Thus, this problem describes a normal distribution with a mean
Question A
Asking what IQ score has 95% of people above it is precisely the same as asking what IQ score has 5% of people below it, since we know that all IQ scores combined would represent 100% of all scores. For the standard normal distribution, we need to know which z-score has a left-tail area that is 0.05; this would be the point where 5% (ie 0.05) of the area under the standard normal distribution lies to the left of that z-score.
To get this, we can either consult a z-score table or use a z-score calculator. I will opt to use a z-score calculator, which finds that a z-score of -1.64 (to two decimals) is our target.
Now, we use the z-score formula to determine the correlated IQ score
Question B
To find the percentage of people who would score less than 90, we work in an opposite direction than Question A. In this case, we will convert the IQ score of
A z-score calculator tells us that for this z-score, approximately 25.3% of all z-scores lie to the left of this z-score. Another way of looking at this is saying that 25.3% of people would be expected to have a lower IQ score than 90.
Question C
This question is more straightforward. We can use the z-score formula to convert an IQ score of 120 from a distribution of