Question: 3. (3 points) Suppose that a normal distribution has a mean of 50 and a standard deviation of 7…

3. (3 points) Suppose that a normal distribution has a mean of 50 and a standard deviation of 7. Convert each raw data score to a z-score. a. 59 b. 50 c. 38

Solution

To convert each raw data score to a z-score, use the formula: \[ z = \frac{x - \mu}{\sigma} \] where \(x\) is the raw score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. Given: \(\mu = 50\), \(\sigma = 7\) a. For \(x = 59\): \[ z = \frac{59 - 50}{7} \] \[ z = \frac{9}{7} \] \[ z \approx 1.29 \] b. For \(x = 50\): \[ z = \frac{50 - 50}{7} \] \[ z = \frac{0}{7} \] \[ z = 0 \] c. For \(x = 38\): \[ z = \frac{38 - 50}{7} \] \[ z = \frac{-12}{7} \] \[ z \approx -1.71 \] Therefore, the z-scores are approximately: a. 1.29 b. 0 c. -1.71