Question
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
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
Answers
GPT 3.5
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
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