Let's address the given problem step by step.
1. Calculate the total number of births:
We are given the frequencies of births on each day of the week: [tex]\(53, 63, 72, 55, 61, 44, 52\)[/tex].
[tex]\[
\text{Total number of births} = 53 + 63 + 72 + 55 + 61 + 44 + 52 = 400
\][/tex]
2. Calculate the relative frequency for each day of the week:
Relative frequency is calculated by dividing the frequency of each day by the total number of births and then converting it to a percentage.
[tex]\[
\text{Relative Frequency on Monday} = \left( \frac{53}{400} \right) \times 100 = 13.25\%
\][/tex]
[tex]\[
\text{Relative Frequency on Tuesday} = \left( \frac{63}{400} \right) \times 100 = 15.75\%
\][/tex]
[tex]\[
\text{Relative Frequency on Wednesday} = \left( \frac{72}{400} \right) \times 100 = 18.00\%
\][/tex]
[tex]\[
\text{Relative Frequency on Thursday} = \left( \frac{55}{400} \right) \times 100 = 13.75\%
\][/tex]
[tex]\[
\text{Relative Frequency on Friday} = \left( \frac{61}{400} \right) \times 100 = 15.25\%
\][/tex]
[tex]\[
\text{Relative Frequency on Saturday} = \left( \frac{44}{400} \right) \times 100 = 11.00\%
\][/tex]
[tex]\[
\text{Relative Frequency on Sunday} = \left( \frac{52}{400} \right) \times 100 = 13.00\%
\][/tex]
Thus, we can construct the relative frequency distribution table:
\begin{tabular}{c|c|l}
\hline Day & \multicolumn{2}{|c}{ Relative Frequency } \\
\hline Monday & 13.25 & [tex]$\%$[/tex] \\
\hline Tuesday & 15.75 & [tex]$\%$[/tex] \\
\hline Wednesday & 18.00 & [tex]$\%$[/tex] \\
\hline Thursday & 13.75 & [tex]$\%$[/tex] \\
\hline Friday & 15.25 & [tex]$\%$[/tex] \\
\hline Saturday & 11.00 & [tex]$\%$[/tex] \\
\hline Sunday & 13.00 & [tex]$\%$[/tex] \\
\hline
\end{tabular}
3. Determine if the frequencies are substantially different:
Frequencies will be considered substantially different if any frequency is at least twice any other frequency.
The minimum frequency is [tex]\(44\)[/tex] (Saturday), and the maximum frequency is [tex]\(72\)[/tex] (Wednesday).
[tex]\[
\text{Twice the minimum frequency} = 2 \times 44 = 88
\][/tex]
Since [tex]\(72\)[/tex] is less than [tex]\(88\)[/tex], no frequency is at least twice any other frequency.
4. Conclusion:
Since no frequency is at least twice any other frequency, it appears that births occur on the days of the week with frequencies that are about the same.
Hence, the correct answer is:
[tex]\[
\text{B. Yes, it appears that births occur on the days of the week with frequencies that are about the same.}
\][/tex]
