Exhibit 5-3
Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.
-Refer to Exhibit 5-3. The variance is
A)1.431
B)2.047
C)3.05
D)21

Question

Exhibit 5-3
Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below. 
-Refer to Exhibit 5-3. The variance is
A)1.431 
B)2.047 
C)3.05 
D)21

Quizplus · Accepted Answer

To find the variance, we first need to calculate the expected value or mean. We can do this by multiplying each possible outcome by its probability and then adding up the results: 
E(X) = (0)(0.20) + (1)(0.25) + (2)(0.30) + (3)(0.15) + (4)(0.05) + (5)(0.03) + (6)(0.02) = 1.68
Next, we can use the formula for variance: 
Var(X) = E(X^2) - [E(X)]^2
We can find E(X^2) by squaring each possible outcome, multiplying by its probability, and adding up the results: 
E(X^2) = (0^2)(0.20) + (1^2)(0.25) + (2^2)(0.30) + (3^2)(0.15) + (4^2)(0.05) + (5^2)(0.03) + (6^2)(0.02) = 4.14
Plugging in the values, we get: 
Var(X) = 4.14 - (1.68)^2 = 2.047
Therefore, the variance is 2.047. The best choice is B.

Exhibit 5-3 Roth Is a Computer-Consulting Firm. the Number of New Clients