Problem
5Z: Topics in Math; Pirnot 6ed. jacotte petit frere $\operatorname{Sec} 14.3-14.4)$ Question 11 of 11 This quiz: 25 point(s) possible This question: 2 point(s) possible Submit quiz Assume that math test scores are normally distributed with a mean of 200 and a sthidard deviation of 40 . If you were to score 120 on this exam, what percentage of those taking the test scored below you? Click the icon to view the table of $z$-scores. What percentage of those taking the test scored below you? $\square \%$ (Round to the nearest tenth as needed.)
Solution
Step 1 ：Calculate the z-score using the formula: \(Z = \frac{X - \mu}{\sigma}\)
Step 2 ：Substitute the given values into the formula: \(Z = \frac{120 - 200}{40} = -2\)
Step 3 ：A z-score of -2 means that the test score of 120 is 2 standard deviations below the mean.
Step 4 ：Use a z-table to find the percentage of test scores that fall below a z-score of -2. The z-table shows that approximately 2.28% of test scores fall below this value.
Step 5 ：\(\boxed{2.3\%}\) (rounded to the nearest tenth) of those taking the test scored below you.
