The Ages of Six Members of a Board of Directors

question 11

Essay

The ages of six members of a board of directors of a nonprofit organization are shown below. $$\begin{array} { r | c c c c c c } \text { Member } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\ \hline \text { Age } & 32 & 52 & 43 & 64 & 41 & 50 \end{array}$$ Consider these board members to be a population of interest. The mean age, µ, for the population is 47. Construct a table that shows all of the possible samples of size four. For each of the possible samples, list the people in the sample, their ages, and the sample mean. The first line of the table is shown below. $$\begin{array} { r | c | c } \text { Sample } & \text { Ages } & \bar { X } \\ \hline \text { A, B, C, D } & 32,52,43,64 & 47.75 \end{array}$$ Use your table to find the probability that, for a random sample of size four, the sample mean will be within 4 years of the population mean.

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Definitions:

Evolutionary Psychologists

Researchers who study how evolutionary principles explain psychological processes and behaviors.

Natural Selection

Natural selection is the process by which organisms better adapted to their environment tend to survive and produce more offspring, a central concept of Charles Darwin's theory of evolution.

Cognitive Mechanisms

Mental processes involved in gaining knowledge and comprehension, including thinking, knowing, remembering, judging, and problem-solving.

Physically Attractive

A characteristic of an individual that is found to be visually appealing to others, often influenced by cultural standards and biological instincts.