To calculate the variance, we first need to calculate the mean or expected value of the number of shoplifting incidents.
Mean (μ) = Σ(x * P(x))
= 0*0.1 + 1*0.2 + 2*0.25 + 3*0.3 + 4*0.15
= 0 + 0.2 + 0.5 + 0.9 + 0.6
= 2.2
Now, we calculate the variance using the formula:
Variance = Σ((x - μ)^2 * P(x))
= (0 - 2.2)^2 * 0.1 + (1 - 2.2)^2 * 0.2 + (2 - 2.2)^2 * 0.25 + (3 - 2.2)^2 * 0.3 + (4 - 2.2)^2 * 0.15
= 4.84 * 0.1 + 1.44 * 0.2 + 0.04 * 0.25 + 0.64 * 0.3 + 3.24 * 0.15
= 0.484 + 0.288 + 0.01 + 0.192 + 0.486
= 1.46
Therefore, the variance for the number of shoplifting incidents during a given day is 1.46, so the correct answer is:
A) 1.46
The following table lists the probability distribution of the number of shoplifting incidents that occur during a day at a certain shopping center:
Number of shoplifting incidents 0 1 2 3 4
Probability 0.1 0.2 0.25 0.3 0.15
Determine the variance for the number of shoplifting incidents during a given day.
A)1.46
B)4.1
C)6.3
D)1.2083
E)2.0248
1 answer