Question

In a geology course, students were learning to use a balance scale to make accurate weighings of rock samples. One student plans to weigh a rock 20 times and then calculate the average of the 20 measurements to estimate her rock's true weight. A second student plans to weigh a rock 5 times and calculate the average of the 5 measurements to estimate his rock's true weight. Which student is more likely to come the closest to the true weight of the rock he or she is weighing

Answer 1

Explanation:

The second student who plans to weigh the rock 5 times and calculate the average of the 5 measurements is more likely to come closer to the true weight of the rock. This is because the concept of the Central Limit Theorem applies here.

The Central Limit Theorem states that the distribution of the sample means of a large enough number of independent, identically distributed random variables will be approximately normally distributed, regardless of the original distribution of the random variables. In this case, the rock's weight measurements can be considered as random variables with some inherent variability.

By taking the average of 5 measurements, the second student is effectively reducing the impact of individual measurement errors and random fluctuations, leading to a more accurate estimate of the true weight. On the other hand, while the first student is taking more measurements (20), if there are significant measurement errors or variations in the equipment or conditions between each measurement, it may not necessarily result in a more accurate estimate of the true weight.

So, the second student's approach of taking 5 measurements and calculating the average is more likely to yield a closer estimate of the true weight of the rock.