In the Old Roman Coliseum, Two Horses Would Be Placed

question 2

Essay

In the old Roman Coliseum, two horses would be placed in tandem (side by side) and hitched to a chariot. Since the fast chariots needed to be able to pass the slow chariots, it was of some importance that the horses have room to run, but also they should not be too large. For chariot hitching purposes, the widest measure across a horse occurs in the rump area. The mean rump width is approximately 27" with a standard deviation of about 2". Let random variable w = width in inches across the rump of a randomly selected horse
a) The usual length measure as it applies to horses is the "hand," which is by definition equal to 4". Define random variable h = width in hands across the rump of a randomly selected horse. What are the mean and standard deviation of h?
b) Suppose horses are randomly chosen for a particular Roman chariot. Define random variable c = h₁ + h₂ to be the rump width of two randomly selected horses. What are the mean and standard deviation of c?
c) Suppose that in the original chariot design a 16 inch separation of the horses is specified so that the horses have room to avoid each other. This leads to random variable a = 16 + w₁ + w₂. Describe how this addition of 16 inches of "wiggle room" would change the mean and standard deviation in part (b). Do not recalculate the mean and standard deviation.

---

Definitions:

Cost-volume-profit

An analysis to determine how changes in costs and volume affect a company's operating income and net income.

Fixed Costs

Costs that do not change in total despite fluctuations in the volume of goods or services produced or sold.

Variable Costs

Charges that fluctuate according to the degree of business operations.

Cost-volume-profit Graph

A graphical representation that shows the relationship between a company's costs, its sales volume, and its profits, used for planning and decision-making.