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a) The mean of the probability distribution = 0.6

b) The variance of the probability distribution = 0.3

c) The standard deviation of the probability distribution = 0.5

Step-by-step explanation:

a) Data and Calculations:

number of dogs per household in a small town

Dogs   Probability  Expected  Mean Diff    Mean Diff.

                               Value                            Squared

0          0.650           0               -0.569         0.32376

1           0.216            0.216        -0.353          0.12461

2         0.087            0.174         -0.395          0.15603

3          0.026            0.078       -0.491            0.24108

4          0.014             0.056       -0.513           0.26317

5          0.009          0.045       -0.524           0.27458

The mean =           0.569 (Sum of expected value)                          

Variance = mean of squared differences = 0.27665 (1.38323/5)

Standard deviation = square root of variance = 0.526 = 0.5