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The Ages of Six Members of a Board of Directors

question 1

Essay

The ages of six members of a board of directors of a nonprofit organization are shown below.
 Member  A  B  C  D  E  F  Age 325243644150\begin{array}{r|cccccc} \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\mu , for the population is 47. Construct a table that shows all of the possible samples of size two. 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.
 Sample  Ages XA,B32,5242\begin{array}{r|r|r} \text { Sample } & \text { Ages } & \overline{\mathrm{X}} \\ \hline \mathrm{A}, \mathrm{B} & 32,52 & 42 \end{array}
Use your table to find the probability that, for a random sample of size two, the sample mean will equal the population mean.

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Definitions:

Registration

The act of recording or enrolling an individual's or entity's details on an official list or registry for legal, security, or operational purposes.

Best Efforts

A clause requiring a party to make the maximum effort to achieve a task, without guaranteeing success.

Underwriting

The process by which insurers evaluate the risks associated with insuring a particular person or asset and decide the premium to charge.

Issuer

An entity that issues and is responsible for the financial instruments like stocks or bonds.

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