The National Collegiate Athletic Association (NCAA) requires Division II athletes to get a combined score of at least 820 on the Mathematics and Critical Reading sections of the SAT exam in order to compete in their first college year. In 2018, the combined scores of the millions of college-bound seniors taking the SATs were approximately Normal with mean 1068 and standard deviation approximately 204. What percentage of all college-bound seniors had scores less than 820 ?

To find the percentage of college-bound seniors with scores less than 820, we can standardize the score using a z-score. The formula for a z-score is: \[ z = \frac{(X - \mu)}{\sigma} \] where \( X \) is the score (820), \( \mu \) is the mean (1068), and \( \sigma \) is the standard deviation (204). Plugging in the numbers: \[ z = \frac{(820 - 1068)}{204} \approx -1.2157 \] Next, we look this z-score up in a standard Normal distribution table or use a calculator to find that about 11.5% of college-bound seniors scored less than 820. So, in a nutshell, only about 11.5% of students were below that minimum score—a reminder that getting past the SAT mountain is crucial for new athletes entering college sports! To help further illustrate, picture this: If you're competing in a race, starting behind the pack can be tough, right? That's a little like these students who scored low on the SAT—it's not the end of the race, but it sure makes the journey ahead a bit more challenging!