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A phlebotomist draws the blood of a random sample of 50 patients and determines their blood types as shown. Complete parts (a) through (o).

\begin{tabular}{lllll}
[tex]$O$[/tex] & [tex]$A$[/tex] & [tex]$A$[/tex] & [tex]$O$[/tex] & [tex]$O$[/tex] \\
[tex]$B$[/tex] & [tex]$O$[/tex] & [tex]$B$[/tex] & [tex]$A$[/tex] & [tex]$O$[/tex] \\
[tex]$B$[/tex] & [tex]$B$[/tex] & [tex]$A$[/tex] & [tex]$B$[/tex] & [tex]$B$[/tex] \\
[tex]$O$[/tex] & [tex]$O$[/tex] & [tex]$O$[/tex] & [tex]$A$[/tex] & [tex]$O$[/tex] \\
[tex]$AB$[/tex] & [tex]$O$[/tex] & [tex]$A$[/tex] & [tex]$B$[/tex] & [tex]$A$[/tex] \\
[tex]$O$[/tex] & [tex]$A$[/tex] & [tex]$A$[/tex] & [tex]$O$[/tex] & [tex]$O$[/tex] \\
[tex]$O$[/tex] & [tex]$A$[/tex] & [tex]$O$[/tex] & [tex]$AB$[/tex] & [tex]$A$[/tex] \\
[tex]$O$[/tex] & [tex]$B$[/tex] & [tex]$A$[/tex] & [tex]$AB$[/tex] & [tex]$O$[/tex] \\
[tex]$O$[/tex] & [tex]$O$[/tex] & [tex]$O$[/tex] & [tex]$O$[/tex] & [tex]$A$[/tex] \\
[tex]$O$[/tex] & [tex]$O$[/tex] & [tex]$A$[/tex] & [tex]$A$[/tex] & [tex]$O$[/tex]
\end{tabular}

(a) Construct a relative frequency distribution. (Type integers or decimals. Do not round.)

\begin{tabular}{|c|c|}
\hline
Blood Type & Relative Frequency \\
\hline
A & [tex]$\square$[/tex] \\
AB & [tex]$\square$[/tex] \\
B & [tex]$\square$[/tex] \\
O & [tex]$\square$[/tex] \\
\hline
\end{tabular}



Answer :

Let's construct the relative frequency distribution table based on the data provided:

1. Total number of samples: 50
2. Frequency of blood types:
- Blood type A: 15
- Blood type AB: 3
- Blood type B: 8
- Blood type O: 24

3. Relative frequency of each blood type:
- Relative frequency of A: [tex]\( \frac{15}{50} = 0.3 \)[/tex]
- Relative frequency of AB: [tex]\( \frac{3}{50} = 0.06 \)[/tex]
- Relative frequency of B: [tex]\( \frac{8}{50} = 0.16 \)[/tex]
- Relative frequency of O: [tex]\( \frac{24}{50} = 0.48 \)[/tex]

Thus, the completed relative frequency distribution table is:

[tex]\[ \begin{tabular}{|c|c|} \hline Blood Type & \begin{tabular}{c} Relative \\ Frequency \end{tabular} \\ \hline A & 0.3 \\ AB & 0.06 \\ B & 0.16 \\ O & 0.48 \\ \hline \end{tabular} \][/tex]

This table provides a clear representation of how the different blood types are distributed in the sample.