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A Village Has Five Residents, Each of Whom Has an Accumulated

question 85

Multiple Choice

A village has five residents, each of whom has an accumulated savings of $50. Each villager can use the money to buy a government bond that pays 10 percent interest per year or to buy a year-old goat, send it onto the commons to graze, and sell it after one year. The price of the goat that the villager will get at the end of the year depends on the amount of weight it gains while grazing on the commons, which in turn depends on the number of goats sent onto the commons, as shown in the table below. Assume that if a villager is indifferent between buying a bond and buying a goat, the villager will buy a goat. $\begin{array} { | c | c | c | } \hline \begin{array} { c } \text { Number af gants } \\\text { an the carmuns }\end{array} & \begin{array} { c } \text { Price per 2-year } \\\text { ald poat (5) }\end{array} & \begin{array} { c } \text { Incame per } \\\text { gant (\$/year) }\end{array} \\\hline 1 & 80 & 30 \\\hline 2 & 75 & 25 \\\hline 3 & 70 & 20 \\\hline 4 & 65 & 15 \\\hline 5 & 55 & 5 \\\hline\end{array}$
When the each villager decides how to invest based on his or her narrow self-interest, total village income will be ________ when the village collectively decides how to invest.

Definitions:

Sign Test Applications

The uses of a nonparametric test that is used to evaluate the difference between the medians of two paired samples.

Normal Approximation

A method used to approximate the distribution of various sample statistics to the normal distribution under certain conditions.

Nonzero Differences

Refers to the outcomes in statistical analyses where the differences between compared measures or values are not equal to zero, indicating variability or effect.

Binomial Distribution

The binomial distribution is a probability distribution that summarizes the likelihood of obtaining a fixed number of successes in a fixed number of trials in a binary context, where there are only two possible outcomes.