At the Last Home Football Game, the Senior Football Players

question 18

Essay

At the last home football game, the senior football players walk through a specially constructed welcoming arch, 2 abreast. It is considered unseemly to bump each other on the way through, so the arch must be wide enough for two players to go through. The distribution of widths of football players with shoulder pads on is approximately normal; the mean padded football player width is 30 inches, and the standard deviation is 5 inches. Let random variable w = width in inches of a randomly selected padded football player.
a) Since this is a statistics test, the carpenter who will be constructing the arch has only metric measuring tools, and must convert all the information above to metric measures. 1 inch = 2.54 centimeters, and we define random variable m = width in centimeters of a randomly selected padded football player. What are the mean and standard deviation of m?
b) Suppose the football players are paired randomly to go through the arch. Define random variable v = w₁ + w₂ to be the collective width (in inches) of two randomly selected football players. What are the mean and standard deviation of v?
c) Suppose that in the original specifications of the arch a 10 inch separation of the football players is specified so that the football players have room to avoid each other. This leads to random variable a = 10 + w₁ + w₂. Describe how this addition of 10 inches of "wiggle room" would change the mean and standard deviation in part (b). Do not recalculate the mean and standard deviation.

---

Definitions:

Optimal R&D

Refers to the ideal level of spending or investment in research and development activities that maximizes innovation benefits relative to costs.

Expected-Rate-Of-Return

The predicted amount of gain or loss an investment is expected to generate, expressed as a percentage.

Interest-Rate Cost-Of-Funds

The expense associated with borrowing funds, measured by the interest rate that banks or other financial institutions charge for the use of their money.

Interest-Rate Cost

The cost incurred by an individual or entity due to the interest rate applied on borrowed funds, influencing how much is paid back in interest over the loan period.