Questions: An airline offers discounted flights from Atlanta to five American cities. Below is a frequency distribution of the number of tickets purchased for each location based on a random sample of purchased tickets. Complete parts (a) through ( f ). Response Frequency ------ Las Vegas 1121 Orlando 1035 New York 956 Chicago 498 San Diego 672 (a) Construct a relative frequency distribution of the data. Response Relative Frequency ------ Las Vegas 0.2620 Orlando 0.2417 New York 0.2232 Chicago 0.1163 San Diego 0.1570 (Round to three decimal places as needed.) (b) What proportion of the tickets were for New York? (Round to three decimal places as needed.)

An airline offers discounted flights from Atlanta to five American cities. Below is a frequency distribution of the number of tickets purchased for each location based on a random sample of purchased tickets. Complete parts (a) through ( f ). Response Frequency ------ Las Vegas 1121 Orlando 1035 New York 956 Chicago 498 San Diego 672 (a) Construct a relative frequency distribution of the data. Response Relative Frequency ------ Las Vegas 0.2620 Orlando 0.2417 New York 0.2232 Chicago 0.1163 San Diego 0.1570 (Round to three decimal places as needed.) (b) What proportion of the tickets were for New York? (Round to three decimal places as needed.)
Transcript text: An airline offers discounted flights from Atlanta to five American cities. Below is a frequency distribution of the number of tickets purchased for each location based on a random sample of purchased tickets. Complete parts (a) through ( $f$ ). \begin{tabular}{|l|c|} \hline \multicolumn{1}{|c|}{ Response } & Frequency \\ \hline Las Vegas & 1121 \\ Orlando & 1035 \\ New York & 956 \\ Chicago & 498 \\ San Diego & 672 \\ \hline \end{tabular} (a) Construct a relative frequency distribution of the data. \begin{tabular}{|l|c|} \hline \multicolumn{1}{|c|}{ Response } & \begin{tabular}{c} Relative \\ Frequency \end{tabular} \\ \hline Las Vegas & 0.2620 \\ Orlando & 0.2417 \\ New York & 0.2232 \\ Chicago & 0.1163 \\ San Diego & 0.1570 \\ \hline \end{tabular} (Round to three decimal places as needed.) (b) What proportion of the tickets were for New York? $\square$ (Round to three decimal places as needed.)
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Solution

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Solution Steps

To solve the given problem, we need to calculate the relative frequency distribution and the proportion of tickets for New York.

(a) To construct a relative frequency distribution, we divide the frequency of each city by the total number of tickets.

(b) The proportion of tickets for New York is calculated by dividing the frequency of New York tickets by the total number of tickets.

Step 1: Calculate Total Number of Tickets

First, we calculate the total number of tickets purchased by summing the frequencies for all cities: \[ \text{Total Tickets} = 1121 + 1035 + 956 + 498 + 672 = 4282 \]

Step 2: Construct Relative Frequency Distribution

To find the relative frequency for each city, divide the frequency of each city by the total number of tickets. The relative frequency for each city is calculated as follows:

  • Las Vegas: \[ \frac{1121}{4282} \approx 0.2618 \]
  • Orlando: \[ \frac{1035}{4282} \approx 0.2417 \]
  • New York: \[ \frac{956}{4282} \approx 0.2233 \]
  • Chicago: \[ \frac{498}{4282} \approx 0.1163 \]
  • San Diego: \[ \frac{672}{4282} \approx 0.1569 \]
Step 3: Calculate Proportion of Tickets for New York

The proportion of tickets purchased for New York is calculated by dividing the frequency of New York tickets by the total number of tickets: \[ \frac{956}{4282} \approx 0.2233 \]

Final Answer

  • The relative frequency distribution is:

    • Las Vegas: \(\boxed{0.2618}\)
    • Orlando: \(\boxed{0.2417}\)
    • New York: \(\boxed{0.2233}\)
    • Chicago: \(\boxed{0.1163}\)
    • San Diego: \(\boxed{0.1569}\)

  • The proportion of tickets for New York is: \(\boxed{0.2233}\)

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