THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency.

-What is the variance of the number of claims processed?
A)3.6211
B)2.0819
C)1.4428
D)1.9029

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The following table presents the probability distribution function for the number of claims processed per hour at an insurance agency.
 
-What is the variance of the number of claims processed?
A)3.6211 
B)2.0819 
C)1.4428 
D)1.9029

Quizplus · Accepted Answer

To find the variance of the number of claims processed, we need to use the following formula:

Variance = ∑(x-μ)²P(x)

Where x is the number of claims processed, μ is the expected value (mean), and P(x) is the probability of processing x number of claims.

We can calculate the expected value as:

μ = ∑xP(x) = 0.7(2) + 0.2(3) + 0.1(4) = 2.2

Now, using the above formula, we get:

Variance = (2-2.2)²(0.7) + (3-2.2)²(0.2) + (4-2.2)²(0.1) = 0.484 + 0.192 + 0.00576 = 0.68276

Therefore, the variance of the number of claims processed is 0.68276, which is closest to option B) 2.0819.