a) Using the normal approximation to the binomial distribution, the probability that among 1,023 randomly selected voters, at least 679 voted is 0.015.
b) The results suggest that the observed proportion of voters among 1023 randomly selected people is significantly higher than the expected proportion of 63%.
a) To find the probability that among 1023 randomly selected voters, at least 679 did vote, calculate the z-score and find the probability using the standard normal distribution by first calculating the mean and standard deviation of the binomial distribution as follows:
Mean (μ) = n * p = 1023 * 0.63
= 643.89
Standard Deviation (σ) = √(n * p * (1 - p))
= √(1023 * 0.63 * 0.37)
= 16.12
The z-score: z = (679 - 643.89) / 16.12 ≈ 2.16
Using a standard normal distribution table or calculator, the probability that at least 679 out of 1023 voted is as follows:
The probability P(Z > 2.16) ≈ 0.015.