Final answer:
The question involves data analysis and statistical interpretation from a healthcare context, requiring the application of mathematical concepts like averages and sampling to provide informed and accurate conclusions.
Step-by-step explanation:
To construct an empirical discrete probability distribution, you can follow these steps:
a. Calculate Relative Frequencies:
Let X represent the number of operating rooms in use.
Count the number of days for each value of X.
Calculate the relative frequency for each value of X using the formula: P(X)= Total number of days/Number of days with X rooms in use
Here's the calculation based on the given data:
X = 1 :P(X=1)= 3/20
X = 2 :P(X=2)= 5/20
X = 3:P(X=3)= 8/20
X = 4 :P(X=4)= 4/20
b. Draw a graph:
Create a bar graph where the x-axis represents the number of operating rooms (X) and the y-axis represents the probability (P(X)).
c. Verify the Conditions for a Valid Discrete Probability Distribution:
The probabilities must be between 0 and 1:
0≤P(X)≤1
The sum of all probabilities must equal 1:
∑P(X)=1
Check that the calculated probabilities meet these conditions.
P(X=1)+P(X=2)+P(X=3)+P(X=4)= 3/20 + 5/20 + 8/20 + 4/20 = 1
Also, ensure that each individual probability is between 0 and 1.
So, the constructed distribution is a valid discrete probability distribution.
Your correct question is: 8. The following data were collected by counting the number of operating rooms in use at
Tampa general Hospital over a 20-day period: On three of the days only one operating
room was used, on five of the days two were used, on eight of the days three were used,
and on four days all four of the hospital’s operating rooms were used.
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. Draw a graph of the probability distribution.
c. Show that your probability distribution satisfies the required conditions for a valid
discrete probability distribution.