7. Twelve nurses work the fourth floor at a hospital, monitoring and assisting p

Question

7. Twelve nurses work the fourth floor at a hospital, monitoring and assisting patients. The nurses are regularly (average 1.3 times per hour each) required to access a drug dispenser on a different floor. Average time (including travel, but not including waiting) for getting drugs from the dispenser is 2.4 minutes. The supervisor has noticed that on occasion more than one nurse is using or waiting for the drug dispenser which reduces the number of nurses that are monitoring the patients on the fourth floor. The supervisor is considering setting up a process to ensure that nurses do not go to the dispenser if there is more than one nurse there already. The goal is to ensure that there is always at least 10 nurses on the fourth floor. Under current conditions, what percentage of the time is there at least 10 nurses on the fourth floor?

a.0%

b.57%

c.67%

d.86%

e.99%

Explanation / Answer

Answer is e. 99%

Probability of at least 10 nurse out of 12 is present in 4th floor = 1 - Probability that either 1 or 2 nurses are not present in the 4th floor.

Now probability that 1 nurse out of 12 is not present = 1/12 = 0.0833

Probability that 2 nurse out of 12 is not present = 2/12 = 0.167

Hence probability that at least 10 nurses are available at 4th floor = 1 - (0.0833 * 0.1667) = 0.987

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