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.

---

Definitions:

Lipoproteins

Lipoproteins are particles made of lipids and proteins that transport fats around the body in the blood.

Golgi Apparatus

An organelle found in most eukaryotic cells, involved in modifying, sorting, and packaging proteins and lipids for secretion or delivery to other organelles.

Proteins and Lipids

Essential biomolecules; proteins are polymers of amino acids functioning in structure and enzymes, while lipids are fatty acids and their derivatives, serving as energy storage and cell membrane components.

Microtubules

Cylindrical structures in the cytoplasm of eukaryotic cells, playing roles in cell shape, intracellular transport, and cell division.