Answer :
The mean (μ) is 807.3, and the standard deviation (σ) is approximately 18.51.
If we use the normal distribution as an approximation to the binomial distribution, we can calculate the mean and standard deviation for the given scenario.
Given:
Probability of success (supporting the incumbent) = 0.59
Number of trials (people polled) = 1370
The mean (μ) of the binomial distribution is calculated as:
μ = n * p
Substituting the values, we have:
μ = 1370 * 0.59
≈ 807.3
Therefore, the mean (μ) is approximately 807.3.
The standard deviation (σ) of the binomial distribution is calculated as:
σ = √(n * p * (1 - p))
Substituting the values, we have:
σ = √(1370 * 0.59 * (1 - 0.59))
≈ √(1370 * 0.59 * 0.41)
≈ √(342.77)
≈ 18.51
Therefore, the standard deviation (σ) is approximately 18.51.
Using the normal distribution as an approximation to the binomial, the mean (μ) is 807.3, and the standard deviation (σ) is approximately 18.51.
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