Understanding the 99.7% Rule in IQ Scores

    Have you ever wondered how we determine where most IQ scores fall within a standard deviation? Let’s break down this intriguing concept with some practical examples. Understanding the empirical rule isn't just for statisticians; it’s a handy tool for any student diving into quantitative literacy. So, grab your calculator, and let’s tackle the question at hand!

    Now, picture this: you're given an IQ test that has a mean score of 95 and a standard deviation of 16. Using these numbers, we can apply the empirical rule—often referred to as the 68-95-99.7 rule. This rule provides a clear guideline on how data is distributed in a bell-shaped curve, or normal distribution, which is fundamental in statistics.

    Here’s the gist: the rule tells us that about 68% of scores will lie within one standard deviation from the mean, 95% will fall within two standard deviations, and notably, about 99.7% of the scores will lie within three standard deviations. That's where the magic happens!

    Let’s crunch some numbers to find out where approximately 99.7% of IQ scores lie. Starting from our mean of 95:
    1. Take one standard deviation below the mean: 95 - (3 × 16) = 95 - 48 = 47.
    2. Next, one standard deviation above the mean: 95 + (3 × 16) = 95 + 48 = 143.

    Voilà! We have our range: approximately 99.7% of IQ scores lie between 47 and 143. This means if you were to gather a bunch of people and record their IQ scores, nearly all (or 99.7%) would fall within this spectrum. Pretty neat, right?

    By figuring this out, we can clearly see why option B, between 47 and 143, is the correct answer when looking at the original question. On the flip side, the other options fall short because they don’t encompass the full range of what’s expected when we apply standard deviation calculations.

    But what does this all mean for students studying for a quantitative literacy exam? Well, mastering these concepts not only boosts your confidence but also equips you with essential skills necessary in various fields, from psychology to economics. Plus, it's kind of fun to see how numbers really do tell stories.

    So next time someone casually mentions IQ scores, you can jump in with a confident, "Well, did you know that roughly 99.7% of scores fall between 47 and 143?" You're not just sharing info; you're showcasing your newfound statistical prowess! 

    Remember, like all useful concepts in statistics, grasping the empirical rule takes a little practice and patience. But once you've got it down, you'll carry that knowledge into future assessments and real-world situations. Statistics might seem daunting, but with tools like this, it becomes a powerful ally in your academic toolkit!