The matrix $N = \left[ {\begin{array}{*{20}{c}}{43}\{27}\end{array}} \right]\;\begin{array}{*{20}{c}}{Males}\{Females}\end{array}$ lists the number of males and females in a group of 70 people. The matrix P that lists the percentage of males and females in the same group of people is given by:

Question

BlackTom AI · Accepted Answer

The question provides a column matrix N = [43; 27], representing the counts of males and females in a group of 70 people, and asks for the matrix P that lists the percentages of males and females in the same group.

First, recall that converting counts to percentages involves dividing each count by the total and then multiplying by 100. Since the total is 70, the conversion factor is 100/70, which scales the counts into percentages.

Option analysis:
- Option: P = (100/70) N
  This option directly applies the conversion factor to the entire count vector N, yielding P = (100/70) [43; 27] = [ (43*100/70); (27*100/70) ] = [61.428...; 38.571...]. These are the percentages of males and females, respectively, in the group. This is the correct transformation from counts to percentages.
- Other options (not provided): If there were any alternative forms that failed to include the correct scaling by 100 or incorrectly used a different total, they would misrepresent the percentage breakdown. For example, using just N without scaling would give raw counts, not percentages, and would not sum to 100 when interpreted as percentages alone unless additionally normalized.

In summary, applying the factor 100/70 to the count vector N converts the counts of males and females into their corresponding percentages, which is exactly what P is defined to be in this context.

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