Question

Assuming that the quantities of solid wastes generated daily at a commercial facility are distributed normally, with a mean value of 10 yd3 and a standard deviation of 7 yd3, what size container would you recommend for this facility? What are the important tradeoffs in the selection of container size?

Answer 1

To determine the appropriate container size, we need to consider the mean value and the standard deviation of the daily solid wastes generated at the commercial facility. Since the data is normally distributed, we can use the following formula to calculate the container size:

Container size = mean + z-score * standard deviation

To determine the appropriate z-score, we need to refer to a standard normal distribution table. Assuming a 95% confidence interval, the z-score would be 1.96. Therefore, the container size would be:

Container size = 10 + 1.96 * 7
Container size = 23.32 yd3

Based on this calculation, we would recommend a container size of 24 yd3 to ensure that it can accommodate the average daily waste generated at the facility.

When selecting a container size, there are several important tradeoffs to consider. A larger container size may be more expensive to purchase and maintain, but it can help reduce the frequency of waste removal and transportation, which can save costs in the long run. On the other hand, a smaller container size may be more affordable, but it may require more frequent waste removal, which can increase transportation costs and result in more greenhouse gas emissions. Additionally, the facility's available storage space and access to waste removal services should also be considered when selecting an appropriate container size.

Answer 2

The distributions of solid wastes produced daily at a commercial facility are normally distributed with a mean of 10 yd3 and a standard deviation of 7 yd3. If you were to make a container size recommendation for this facility, what size would you propose? What important tradeoffs should be considered when selecting the size of the container?

It's quite perplexing to determine the perfect size of container for a facility whose waste quantity varies and is subject to changes frequently. A certain degree of burstiness is present in the distribution of solid waste generated on a daily basis in a commercial facility. However, using the available mean and standard deviation values, we can infer that a container size of 24 yd3 should be sufficient to hold the daily waste generated, considering that it's two standard deviations above the mean.

When selecting a container size, various tradeoffs must be considered. A large container is more efficient, as it would not require to be emptied as frequently, but it might be expensive and may take up more space. A smaller container may be less expensive and take up less space, but it would need to be emptied more frequently, which can result in higher transportation costs and more time spent on waste management. It is therefore essential to strike a balance between the frequency of emptying and the container size to ensure that the waste is managed effectively and efficiently.