Question

On the midnight shift, the number of patients with head trauma in the emergency room has the probability distribution shown below:

P(X)
0 0.14
1 0.45
2 0.32
3 0.09

Calculate the mean number of patients with head trauma

Answer 1

To find the mean number of patients with head trauma, we perform a weighted sum of each patient count by its probability. The mean number of patients calculated for the midnight shift is 1.36.

Step-by-step explanation:

To calculate the mean number of patients with head trauma, we multiply each number of patients (X) by its corresponding probability (P(X)), and then sum these products. This is also known as the expected value E(X).

E(X) = Σ [X × P(X)]

The given probability distribution is:

• 
  
• 
  
• 
  
• 
  

So the calculation is:

E(X) = (0 × 0.14) + (1 × 0.45) + (2 × 0.32) + (3 × 0.09)

E(X) = 0 + 0.45 + 0.64 + 0.27

E(X) = 1.36

The mean number of patients with head trauma during the midnight shift is 1.36.