The scores on a test are normally distributed with a mean of 30 and a standard deviation of 6. What is the score that is 1 standard deviation below the mean? A score of \( \square \) is 1 standard deviation below the mean.

To find the score that is 1 standard deviation below the mean, you simply subtract the standard deviation from the mean. In this case, the mean is 30, and the standard deviation is 6. So you calculate: \( 30 - 6 = 24 \). Therefore, a score of 24 is 1 standard deviation below the mean. Historically, the notion of the normal distribution dates back to the 18th century and was popularized by mathematician Carl Friedrich Gauss. He used it to describe the distribution of errors in measurements, which is why it's sometimes referred to as the "Gaussian distribution." This statistical concept has become fundamental in various fields, from psychology to finance! When working with normal distribution, a common mistake is misinterpreting the standard deviation. People often think that it defines a specific score, but it's actually a measure of variability. It’s crucial to remember that the distance between the mean and the score is what the standard deviation quantifies, and this is where many get tripped up!