1. The problem involves analyzing the data set: 108, 200, 310, 150, 180, 119, 160, 180, 201, 190, 280, 202. We will calculate z-scores for these data points considering both population and sample scenarios.\n\n2. First, compute the mean (average) of the data:\n $$\text{Mean} = \frac{108 + 200 + 310 + 150 + 180 + 119 + 160 + 180 + 201 + 190 + 280 + 202}{12} = \frac{2290}{12} = 190.83$$\n\n3. Calculate the variance for the population (using denominator $N=12$):\n $$\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}$$\nCalculate each squared deviation and sum:\n $$\sum (x_i - \mu)^2 = (108 - 190.83)^2 + (200 - 190.83)^2 + \dots + (202 - 190.83)^2 = 26780.91$$\n Therefore, population variance:\n$$\sigma^2 = \frac{26780.91}{12} = 2231.74$$\nPopulation standard deviation:\n$$\sigma = \sqrt{2231.74} = 47.27$$\n\n4. Calculate the variance for the sample (using denominator $n-1=11$):\n$$s^2 = \frac{26780.91}{11} = 2434.63$$\nSample standard deviation:\n$$s = \sqrt{2434.63} = 49.34$$\n\n5. Calculate z-score for a data point $x$ as:\n For population: $$z = \frac{x - \mu}{\sigma}$$\nFor sample: $$z = \frac{x - \mu}{s}$$\n\n6. Example: Calculate z-score for $x=200$:\nPopulation z-score:\n$$z = \frac{200 - 190.83}{47.27} = 0.194$$\nSample z-score:\n$$z = \frac{200 - 190.83}{49.34} = 0.186$$\n\n7. These steps apply to each data point to find their respective z-scores in population and sample contexts.\n\nFinal: The computed mean is approximately 190.83, population standard deviation about 47.27, and sample standard deviation about 49.34. Use these to find z-scores for any data point accordingly.