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Choose the best answers. A spinner has the following outcomes and probabilities: X: 1 2 3 4 5 6 7 8 P(X):...

1. Choose the best answers.
A spinner has the following outcomes and probabilities:
X: 1 2 3 4 5 6 7 8
P(X): 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8
Mean:
Variance:
Standard deviation:

Answer

Mean: The mean of a uniform distribution is the average of the outcomes. For this spinner, the mean is (1+2+3+4+5+6+7+8)/8 = 4.5.

Variance: The variance is calculated using the formula for a uniform distribution: (n^2 - 1)/12, where n is the number of outcomes. Here, n = 8, so variance = (8^2 - 1)/12 = 63/12 = 5.25.

Standard deviation: The standard deviation is the square root of the variance. So, standard deviation = √5.25 ≈ 2.29.

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