Question

In a local hospital, a nurse administrator needs to know how many times per shift a nurse is called for on average by the patients on the floor, in order to determine how much staff is needed per shift. Through tracking the number of times the nurse bell is rung for 100 patients, the following PDF was constructed:

X = number of times the bell is rung
x P(x)
0 10/100
1 30/100
2 25/100
3 20/100
4 10/100
5 5/100
What is the expected value for the average number of times that the bell is rung? Show your equation and your final answer.

Answer 1

The expected value for the average number of times the bell is rung is 2.05.

Step-by-step explanation:

To find the expected value for the average number of times that the bell is rung, we need to multiply each value of X by its corresponding probability, and then sum up the results. The formula for expected value is E(X) = Σ(x * P(x)). In this case, we have:

1. Expected value (E(X)) = (0 * 10/100) + (1 * 30/100) + (2 * 25/100) + (3 * 20/100) + (4 * 10/100) + (5 * 5/100)
2. Evaluating the above expression, we get:
3. E(X) = 0 + 0.3 + 0.5 + 0.6 + 0.4 + 0.25
4. E(X) = 2.05