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Choose the best answer. A spinner has the following outcomes and probabilities. X: 1, 2, 3, 4 P(X): 1/4,...

12. Choose the best answer.
A spinner has the following outcomes and probabilities.
X: 1, 2, 3, 4
P(X): 1/4, 1/4, 1/4, 1/4
Mean:
Variance:
Standard deviation:

Answer

Mean: The mean is calculated as the sum of each outcome multiplied by its probability. Mean = (1 * 1/4) + (2 * 1/4) + (3 * 1/4) + (4 * 1/4) = 2.5

Variance: The variance is calculated as the sum of the squared difference between each outcome and the mean, multiplied by its probability. Variance = ((1 - 2.5)^2 * 1/4) + ((2 - 2.5)^2 * 1/4) + ((3 - 2.5)^2 * 1/4) + ((4 - 2.5)^2 * 1/4) = 1.25

Standard deviation: The standard deviation is the square root of the variance. Standard deviation = √1.25 ≈ 1.12

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