The following data were collected by counting the number of operating rooms in use atTampa general Hospital over a 20-day period: On three of the days only one operatingroom 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 probabilitydistribution 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 validdiscrete probability distribution.

a)

Operating room x    1         2      3       4

P(x)                          0.15  0.25  0.4   0.2

b)

The graph of probability distribution is in attached image.

c)

All the probabilities lies in the range (0 to 1) and the probabilities add up to 1 so, the computed probability distribution is the valid probability distribution.

Step-by-step explanation:

Number of operating rooms   Days

1                                                  3

2                                                 5

3                                                 8

4                                                 4

a)

Sum of frequencies=1+2+3+4=10

Operating rooms x   frequency f  Relative frequency

1                                    3                    3/20=0.15

2                                   5                   5/20=0.25

3                                   8                   8/20=0.4

4                                   4                   4/20=0.2

So, using the relative frequency approach, a discrete probability distribution for number of operating rooms in use on any given day is

Operating room x    1         2      3       4

P(x)                          0.15  0.25  0.4   0.2

b)

The graph of probability distribution is in attached image.

c)

There are two conditions for a probability distribution to be valid

1. All probability must ranges from 0 to 1.

2. All probabilities must add up to 1.

We can see that all the probabilities lies in the range (0 to 1), so, condition 1 is satisfied.

For condition 2,

sum[p(x)]= 0.15+0.25+0.4+0.2=0.4+0.6=1.

As the probabilities add up to 1, so the condition 2 is also satisfied.

Thus, the computed probability distribution is the valid probability distribution.

step-by-step explanation:

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