Awards Committees Need to Be Formed to Review Potential Award

question 12

Essay

Awards committees need to be formed to review potential award recipients. In the past, three people have been assigned to review each applicant. The only stipulation is that a reviewer cannot be assigned to an applicant if the applicant is a co-worker. The matrix below shows 9 reviewers, 3 candidates, and a matrix. If an entry in the matrix contains an "X", then that specific reviewer is ineligible to review an applicant's material. For example, reviewer 1 cannot review materials submitted by candidate B. It is possible that some reviewers may not receive an assignment.
Applicant
$$\begin{array} { | c | c | c | c | } \hline \text { Reviewer } & \text { A } & \text { B } & \text { C } \\\hline 1 & & \mathrm { X } & \\\hline 2 & \mathrm { X } & & \\\hline 3 & & & \mathrm { X } \\\hline 4 & & & \\\hline 5 & \mathrm { X } & & \\\hline 6 & & \mathrm { X } & \\\hline 7 & & \mathrm { X } & \\\hline 8 & & & \mathrm { X } \\\hline 9 & & \mathrm { X } & \\\hline\end{array}$$
-The committee would like to assign three reviewers to each applicant. A partial solution to this problem is shown below, where the number 1 indicates when a reviewer is assigned to an applicant. Assign reviewers to Applicant B and Applicant C.
Applicant
$$\begin{array} { | c | c | c | c | } \hline \text { Reviewer } & \mathrm { A } & \mathrm { B } & \mathrm { C } \\\hline 1 & & \mathrm { X } & \\\hline 2 & \mathrm { X } & & \\\hline 3 & 1 & & \mathrm { X } \\\hline 4 & 1 & & \\\hline 5 & \mathrm { X } & & \\\hline 6 & & \mathrm { X } & \\\hline 7 & & \mathrm { X } & \\\hline 8 & & & \mathrm { X } \\\hline 9 & 1 & \mathrm { X } & \\\hline\end{array}$$

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Definitions:

Normally Distributed

A data distribution that is symmetrically shaped like a bell curve, with most data points clustering around a central mean value.

Sampling Distribution

The probability distribution of a statistic based on a large number of samples or simulations.

Sample Size

The number of observations or participants used in a study or experiment.

Negatively Skewed Distribution

A distribution with a tail that is longer on the left side, indicating that the bulk of the values are concentrated on the right.