Question

2. The following data were collected by counting the number of operating rooms in use at a 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.

Answer 1

Solution

The following data were collected by counting the number of perating rooms in use at a hospital over a 20 day period:

a)

Let X represents the number of operating rooms in use on any given day

X takes values 1,2,3,4

The probability distribution of X is as follows:

Variable value Days f(x) 13 3/20=0.15 5 5/20=0.25 8 8/20=0.40 4/20=0.20

b)

c) All the values of f(x) are between 0 and 1 sum up 1. Hence it is valid function.