16. A score that is 10 points above the mean corresponds to a \( z \)-score of \( z=+1.20 \). What is the sample standard deviation?

To find the sample standard deviation, you can use the formula for the z-score, which is \( z = \frac{(X - \mu)}{\sigma} \), where \( X \) is the score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. Given that \( z = +1.20 \) and the score is 10 points above the mean, we can say: \[ 1.20 = \frac{(10)}{\sigma} \] From this, rearranging gives: \[ \sigma = \frac{10}{1.20} \approx 8.33 \] So, the sample standard deviation is approximately 8.33 points. Did you know that z-scores are incredibly useful in various fields, like psychology and education, to assess how far away a particular score is from the average? This statistical method helps educators understand student performance relative to their peers! Another fun fact: The concept of standard deviation can be traced back to the early 20th century when statisticians like Karl Pearson and Ronald Fisher began formalizing statistical methods. Today, it’s a cornerstone of statistics used in everything from finance to quality control!