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Answer question 4.2.1 by determining the probability.

Mathematics

ScanSolve AI Answer

Answer

1.0
200

not valid\text{not valid}

Step-by-step solution

5 steps
  1. Answer question 4.2.1 by determining the probability.

    The capacity of a cinema-style venue is 400 guests. A function is suitable if the number of guests is less than or equal to 400.

    List of guests for 2023: 180,350,400,200,215,90,150,230,160180, 350, 400, 200, 215, 90, 150, 230, 160.
    All 9 of these values are ≤400\le 400.

    List of guests for 2022: 360,160,300,70,160,200,240360, 160, 300, 70, 160, 200, 240.
    All 7 of these values are ≤400\le 400.

    Total number of functions = 9(for 2023)+7(for 2022)=169 (\text{for } 2023) + 7 (\text{for } 2022) = 16.
    Number of functions suitable for a cinema-style venue = 9+7=169 + 7 = 16.

    The probability is the number of suitable functions divided by the total number of functions.

    Probability=1616=1\text{Probability} = \frac{16}{16} = 1

    As a decimal, the probability is 1.0\boxed{1.0}.

  2. Answer question 4.2.2 by determining the median number of guests for 2023.

    First, list the number of guests for 2023 in ascending order:
    90,150,160,180,200,215,230,350,40090, 150, 160, 180, 200, 215, 230, 350, 400
    There are 9 data points. The median is the middle value, which is the 9+12=5\frac{9+1}{2} = 5-th value.
    The 5th value in the ordered list is 200.
    The median number of guests accommodated during 2023 is 200\boxed{200}.

  3. Answer question 4.2.3 by calculating the range for 2022.

    The number of guests for 2022 are: 360,160,300,70,160,200,240360, 160, 300, 70, 160, 200, 240.
    To find the range, identify the maximum and minimum values.
    Maximum number of guests in 2022 = 360.
    Minimum number of guests in 2022 = 70.

    Range (2022)=Maximum−Minimum\text{Range (2022)} = \text{Maximum} - \text{Minimum} Range (2022)=360−70=290\text{Range (2022)} = 360 - 70 = 290
  4. Calculate the range for 2023.

    The number of guests for 2023 are: 180,350,400,200,215,90,150,230,160180, 350, 400, 200, 215, 90, 150, 230, 160.
    Maximum number of guests in 2023 = 400.
    Minimum number of guests in 2023 = 90.

    Range (2023)=Maximum−Minimum\text{Range (2023)} = \text{Maximum} - \text{Minimum} Range (2023)=400−90=310\text{Range (2023)} = 400 - 90 = 310
  5. Verify the manager's statement.

    The manager stated that the range for 2022 is the same as the range for 2023.
    Range (2022) = 290.
    Range (2023) = 310.
    Since 290≠310290 \neq 310, the ranges are not the same.
    Therefore, the manager's statement is not valid\boxed{\text{not valid}}.

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