To calculate the standard deviation, we first need to find the mean of the distribution.
Mean (μ) = Σ(x * P(x)), where x represents the number of shoplifting incidents and P(x) is the probability of that number of incidents occurring.
Mean = (0 * 0.1) + (1 * 0.2) + (2 * 0.25) + (3 * 0.3) + (4 * 0.15)
Mean = 0 + 0.2 + 0.5 + 0.9 + 0.6
Mean = 2.2
Next, we calculate the variance using the formula:
Variance (σ^2) = Σ((x - μ)^2 * P(x))
Variance = ((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)
Variance = (2.2^2 * 0.1) + (1.2^2 * 0.2) + (0.2^2 * 0.25) + (0.8^2 * 0.3) + (1.8^2 * 0.15)
Variance = (4.84 * 0.1) + (1.44 * 0.2) + (0.04 * 0.25) + (0.64 * 0.3) + (3.24 * 0.15)
Variance = 0.484 + 0.288 + 0.01 + 0.192 + 0.486
Variance = 1.44
Finally, the standard deviation is the square root of the variance:
Standard Deviation = √1.44
Standard Deviation = 1.2
Therefore, the standard deviation for the number of shoplifting incidents during a given day is 1.2.
The closest option provided is 1.21, which is the correct answer.
he 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 standard deviation for the number of shoplifting incidents during a given day.
1.43
2.51
1.1
2.02
1.21
1 answer
1 answer