Suppose the modified quota is 6.47. Fill in the blanks, and round your answers to two decimal places.

(a) Find the lower quota.


(b) Find the upper quota.


(c) Find the arithmetic mean of the lower and upper quotas.


(d) Find the geometric mean of the lower and upper quotas.


(e) Round the given modified quota by comparing it with the arithmetic mean.


(f) Round the given modified quota by comparing it with the geometric mean.

To answer these questions, we need to understand what the terms "lower quota," "upper quota," "arithmetic mean," and "geometric mean" mean in this context.

The modified quota is 6.47, and we need to find the lower quota, upper quota, arithmetic mean, and geometric mean.

(a) The lower quota is the largest whole number that is less than or equal to the modified quota. In this case, it would be 6.

(b) The upper quota is the smallest whole number that is greater than or equal to the modified quota. In this case, it would be 7.

(c) The arithmetic mean is the average of the lower and upper quotas. To find it, we add the lower and upper quotas together and divide by 2. In this case, it would be (6 + 7) / 2 = 13 / 2 = 6.5.

(d) The geometric mean is the square root of the product of the lower and upper quotas. To find it, we multiply the lower and upper quotas together and take the square root. In this case, it would be √(6 * 7) = √42 ≈ 6.48.

(e) To round the modified quota by comparing it with the arithmetic mean, we would compare the difference between the modified quota and the arithmetic mean. If the difference is less than or equal to 0.5, we round down to the arithmetic mean. If the difference is greater than 0.5, we round up to the arithmetic mean plus 1. In this case, the difference between 6.47 and 6.5 is less than 0.5, so we round down to 6.5.

(f) To round the modified quota by comparing it with the geometric mean, we would compare the difference between the modified quota and the geometric mean. If the difference is less than or equal to 0.5, we round down to the geometric mean. If the difference is greater than 0.5, we round up to the geometric mean plus 1. In this case, the difference between 6.47 and 6.48 is less than 0.5, so we round down to 6.48.

So, to summarize:
(a) The lower quota is 6.
(b) The upper quota is 7.
(c) The arithmetic mean is 6.5.
(d) The geometric mean is 6.48.
(e) The modified quota rounded to the arithmetic mean is 6.5.
(f) The modified quota rounded to the geometric mean is 6.48.