Question

The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On four of the days only one operating room was used, on six of the days two were used, on seven of the days three were used, and on three days all four of the hospital's operating rooms were used. Round your answers to two decimal places. a. Use the relative frequency approach to construct an empirical discrete probability distribution for the number of operating rooms in use on any given day. b. Select a graph of the probability distribution. C. Show that your probability distribution satisfies the required conditions for a valid discrete probability distribution. f(x) 0 for x=1,2,3,4 and ∑f(x)=f(1)+f(2)+f(3)+f(4)=1

Answer 1

To construct the empirical discrete probability distribution using the relative frequency approach, calculate the relative frequency for each category by dividing the frequency by the total number of days. Check if the probability distribution satisfies the required conditions: f(x) = 0 for x = 1, 2, 3, 4 and ∑f(x) = 1.

Step-by-step explanation:

To construct the empirical discrete probability distribution using the relative frequency approach, we need to calculate the relative frequency for each category. The relative frequency is calculated by dividing the frequency of each category by the total number of days. In this case, we have:

• Category 1: Frequency = 4, Relative Frequency = 4/20 = 0.2
• Category 2: Frequency = 6, Relative Frequency = 6/20 = 0.3
• Category 3: Frequency = 7, Relative Frequency = 7/20 = 0.35
• Category 4: Frequency = 3, Relative Frequency = 3/20 = 0.15

Now, let's check if the probability distribution satisfies the required conditions:

• f(x) = 0 for x = 1, 2, 3, 4 (which means the probability of having a certain number of operating rooms in use is 0 for numbers other than 1, 2, 3, or 4)
• ∑f(x) = f(1) + f(2) + f(3) + f(4) = 0.2 + 0.3 + 0.35 + 0.15 = 1 (which means the sum of probabilities for all possible outcomes equals 1)