Questions: Hospital admissions: The following frequency distribution presents the five most frequent reasons for h in U.S. community hospitals in a recent year. Reason Frequency (in thousands) Congestive heart failure 923 Coronary atherosclerosis 1344 Heart attack 706 Infant birth 4233 Pneumonia 1147 (a) Construct a relative frequency distribution. Round the answers to two decimal places. Reason Relative Frequency Congestive heart failure Coronary atherosclerosis Heart attack Infant birth Total

Hospital admissions: The following frequency distribution presents the five most frequent reasons for h in U.S. community hospitals in a recent year. Reason Frequency (in thousands) Congestive heart failure 923 Coronary atherosclerosis 1344 Heart attack 706 Infant birth 4233 Pneumonia 1147 (a) Construct a relative frequency distribution. Round the answers to two decimal places. Reason Relative Frequency Congestive heart failure Coronary atherosclerosis Heart attack Infant birth Total
Transcript text: Hospital admissions: The following frequency distribution presents the five most frequent reasons for $h$ in U.S. community hospitals in a recent year. \begin{tabular}{lc} \hline Reason & \begin{tabular}{c} Frequency \\ (in thousands) \end{tabular} \\ \hline Congestive heart failure & 923 \\ Coronary atherosclerosis & 1344 \\ Heart attack & 706 \\ Infant birth & 4233 \\ Pneumonia & 1147 \\ \hline \end{tabular} (a) Construct a relative frequency distribution. Round the answers to two decimal places. \begin{tabular}{lr} \hline Reason & \begin{tabular}{c} Relative \\ Frequency \end{tabular} \\ \hline Congestive heart failure & $\square$ \\ Coronary atherosclerosis & $\square$ \\ Heart attack & $\square$ \\ Infant birth & $\square$ \\ \hline Total & $\square$ \\ \hline \end{tabular}
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Solution

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Solution Steps

To construct a relative frequency distribution, first calculate the total frequency by summing up all the given frequencies. Then, for each reason, divide its frequency by the total frequency to get the relative frequency. Round each result to two decimal places.

Step 1: Calculate Total Frequency

To find the total frequency, sum all the given frequencies: \[ 923 + 1344 + 706 + 4233 + 1147 = 8353 \]

Step 2: Calculate Relative Frequencies

For each reason, divide its frequency by the total frequency and round to two decimal places:

  • Congestive heart failure: \[ \frac{923}{8353} \approx 0.11 \]

  • Coronary atherosclerosis: \[ \frac{1344}{8353} \approx 0.16 \]

  • Heart attack: \[ \frac{706}{8353} \approx 0.08 \]

  • Infant birth: \[ \frac{4233}{8353} \approx 0.51 \]

  • Pneumonia: \[ \frac{1147}{8353} \approx 0.14 \]

Final Answer

The relative frequency distribution is:

  • Congestive heart failure: \(\boxed{0.11}\)
  • Coronary atherosclerosis: \(\boxed{0.16}\)
  • Heart attack: \(\boxed{0.08}\)
  • Infant birth: \(\boxed{0.51}\)
  • Pneumonia: \(\boxed{0.14}\)
  • Total: \(\boxed{1.00}\)
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