Given the mean and standard deviation of a normally distributed set of scores, determine the approximate location of the given scores in terms of the standarc deviation. (8 points) \( \begin{array}{ll}\text { 1. } \mu=27 ; \sigma=6 ; x=18 & \text { 2. } \mu=80 ; \sigma=3 ; x=88\end{array} \)

To find the location of the given scores in terms of standard deviations from the mean, you can use the formula: \( z = \frac{x - \mu}{\sigma} \) 1. For the first score: \( \mu = 27 \), \( \sigma = 6 \), \( x = 18 \) \( z = \frac{18 - 27}{6} = \frac{-9}{6} = -1.5 \) This means the score of 18 is 1.5 standard deviations below the mean. 2. For the second score: \( \mu = 80 \), \( \sigma = 3 \), \( x = 88 \) \( z = \frac{88 - 80}{3} = \frac{8}{3} \approx 2.67 \) This indicates the score of 88 is approximately 2.67 standard deviations above the mean.