The scores on a test are normally distributed with a mean of 150 and a standard deviation of 12 . What is the score that is \( 2 \frac{1}{2} \) standard deviations below the mean? 138 120 180 132

To find the score that is \(2 \frac{1}{2}\) standard deviations below the mean, you need to multiply the number of standard deviations (2.5) by the standard deviation (12) and then subtract that from the mean (150). First, calculate \(2.5 \times 12 = 30\). Then, subtract this from the mean: \(150 - 30 = 120\). Thus, the score that is \(2 \frac{1}{2}\) standard deviations below the mean is 120. Now you’ve cracked it! It’s all about understanding how z-scores relate to the normal distribution, making statistics feel less scary. Think of the standard deviation as the way to navigate how far you can go from the average, like mini-trips from the central hub of 150. Feeling intrigued? Dive into more about normal distributions and their properties! There are plenty of fascinating resources online, including interactive data visualization tools that show how adjustment of mean and standard deviation affects the spread and shape of the distribution. You're on a remarkable journey of statistical discovery!