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. The variance is
A) 1.45.
B) 2.09.
C) 3.1.
D) 9.61.

Question

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.  ​ The variance is
A) 1.45. 
B) 2.09. 
C) 3.1. 
D) 9.61.

Quizplus · Accepted Answer

To find the variance, we need to first find the expected value or mean, which can be calculated as:
(0*0.05)+(1*0.10)+(2*0.15)+(3*0.30)+(4*0.25)+(5*0.10)+(6*0.05)= 3.15
Then, using the formula for variance (σ^2= Σ [Xi - μ]^2 * P(Xi)), we can calculate:
(0-3.15)^2*0.05 + (1-3.15)^2*0.10 + (2-3.15)^2*0.15 + (3-3.15)^2*0.30 + (4-3.15)^2*0.25 + (5-3.15)^2*0.10 + (6-3.15)^2*0.05 = 2.09
Therefore, the answer is B.

Roth Is a Computer-Consulting Firm