Answer question 4.2.1 by determining the probability.

You're on a roll — Step 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, 160. All 9 of these values are 400. List of guests for 2022: 360, 160, 300, 70, 160, 200, 240. All 7 of these values are 400. Total number of functions = 9 (for 2023) + 7 (for 2022) = 16. Number of functions suitable for a cinema-style venue = 9 + 7 = 16. The probability is the number of suitable functions divided by the total number of functions. Probability = (16)/(16) = 1 As a decimal, the probability is 1.0. Step 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, 400 There are 9 data points. The median is the middle value, which is the (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. Step 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, 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 Range (2022) = 360 - 70 = 290 Step 4: Calculate the range for 2023. The number of guests for 2023 are: 180, 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 Range (2023) = 400 - 90 = 310 Step 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 ≠ 310, the ranges are not the same. Therefore, the manager's statement is not valid. What's next?