In a training course offered by a company to a group of workers, one theoretical and the other practical, a rating was given on a scale of 0 to 10. One of the workers received scores of 8.2 and 6.8 in the respective courses. The worker was able to determine the averages and the spread of the grades obtained in each course, with the following result: Theoretical course mean = 8.7 and standard deviation = 0.8 Practical course mean = 5.8 and variance = 1.21. According to the data in the table, in which of the courses did this worker achieve a better relative position?

To determine in which of the courses the worker achieved a better relative position, we can calculate their z-scores for each course. A z-score represents the number of standard deviations a data point is from the mean. A higher z-score indicates a better relative position compared to the rest of the group. For the theoretical course, the worker’s z-score is calculated as follows: z = (x - μ) / σ where x is the worker’s score, μ is the mean, and σ is the standard deviation. Plugging in the given values, we get: z = (8.2 - 8.7) / 0.8 ≈ -0.625 For the practical course, we first need to calculate the standard deviation from the given variance. The standard deviation is the square root of the variance, so in this case it is sqrt(1.21) ≈ 1.1. The worker’s z-score for the practical course is then calculated as follows: z = (x - μ) / σ where x is the worker’s score, μ is the mean, and σ is the standard deviation. Plugging in the given values, we get: z = (6.8 - 5.8) / 1.1 ≈ 0.909 Comparing these two z-scores, we can see that the worker achieved a better relative position in the practical course, where their z-score was higher