The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On five of the days only one operating room was used, on four of the days two were used, on eight of the days three were used, and on three 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. x f(x) 1 2 3 4 (b) Draw a graph of the probability distribution. A graph with 4 bars of unequal heights is given. The horizontal axis is labeled x. The vertical axis is labeled f(x). The first bar on the left is labeled 1 and has a height of approximately 0.15. The second bar from the left is labeled 2 and has a height of approximately 0.20. The third bar from the left is labeled 3 and has a height of approximately 0.25. The fourth bar from the left is labeled 4 and has a height of approximately 0.40. A graph with 4 bars of unequal heights is given. The horizontal axis is labeled x. The vertical axis is labeled f(x). The first bar on the left is labeled 1 and has a height of approximately 0.25. The second bar from the left is labeled 2 and has a height of approximately 0.20. The third bar from the left is labeled 3 and has a height of approximately 0.40. The fourth bar from the left is labeled 4 and has a height of approximately 0.15. A graph with 4 bars of unequal heights is given. The horizontal axis is labeled x. The vertical axis is labeled f(x). The first bar on the left is labeled 1 and has a height of approximately 0.15. The second bar from the left is labeled 2 and has a height of approximately 0.40. The third bar from the left is labeled 3 and has a height of approximately 0.20. The fourth bar from the left is labeled 4 and has a height of approximately 0.25. A graph with 4 bars of unequal heights is given. The horizontal axis is labeled x. The vertical axis is labeled f(x). The first bar on the left is labeled 1 and has a height of approximately 0.40. The second bar from the left is labeled 2 and has a height of approximately 0.25. The third bar from the left is labeled 3 and has a height of approximately 0.20. The fourth bar from the left is labeled 4 and has a height of approximately 0.15. (c) Show that your probability distribution satisfies the required conditions for a valid discrete probability distribution. We have that f(x) ? = ≤ ≥ 0 for x = 1, 2, 3, 4 and f(x) = so the probability distribution satisfies the required conditions for a valid discrete probability distribution.

Name: The following data were collected by counting the number of operating
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On five of the days only one operating room was used, on four of the days two were used, on eight of the days three wer

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 five of the days only one operating room was used, on four of the days two were used, on eight of the days three were used, and on three 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.

x	f(x)
1
2
3
4

(b)

Draw a graph of the probability distribution.

A graph with 4 bars of unequal heights is given. The horizontal axis is labeled x. The vertical axis is labeled f(x).

The first bar on the left is labeled 1 and has a height of approximately 0.15.
The second bar from the left is labeled 2 and has a height of approximately 0.20.
The third bar from the left is labeled 3 and has a height of approximately 0.25.
The fourth bar from the left is labeled 4 and has a height of approximately 0.40.

A graph with 4 bars of unequal heights is given. The horizontal axis is labeled x. The vertical axis is labeled f(x).

The first bar on the left is labeled 1 and has a height of approximately 0.25.
The second bar from the left is labeled 2 and has a height of approximately 0.20.
The third bar from the left is labeled 3 and has a height of approximately 0.40.
The fourth bar from the left is labeled 4 and has a height of approximately 0.15.

A graph with 4 bars of unequal heights is given. The horizontal axis is labeled x. The vertical axis is labeled f(x).

The first bar on the left is labeled 1 and has a height of approximately 0.15.
The second bar from the left is labeled 2 and has a height of approximately 0.40.
The third bar from the left is labeled 3 and has a height of approximately 0.20.
The fourth bar from the left is labeled 4 and has a height of approximately 0.25.

A graph with 4 bars of unequal heights is given. The horizontal axis is labeled x. The vertical axis is labeled f(x).

The first bar on the left is labeled 1 and has a height of approximately 0.40.
The second bar from the left is labeled 2 and has a height of approximately 0.25.
The third bar from the left is labeled 3 and has a height of approximately 0.20.
The fourth bar from the left is labeled 4 and has a height of approximately 0.15.

(c)

Show that your probability distribution satisfies the required conditions for a valid discrete probability distribution.

We have that

f(x) ? = ≤ ≥ 0

for

x = 1, 2, 3, 4

and