Problem
Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 101 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged $18-24,22 \%$ of them voted. Probability that fewer than 25 voted The probability that fewer than 25 of 101 eligible voters voted is (Round to four decimal places as needed.)
Solution
Step 1 ：Calculate the mean (μ) and standard deviation (σ) of the binomial distribution: μ = n * p = 101 * 0.22 = 22.22, σ = \( \sqrt{n * p * (1 - p)} \) = \( \sqrt{101 * 0.22 * (1 - 0.22)} \) = 4.163
Step 2 ：Find the z-score: z = (x - μ) / σ = (25 - 22.22) / 4.163 = 0.6678
Step 3 ：Use a z-table or Python function to find the probability corresponding to the z-score: probability = 0.7479
Step 4 ：\( \boxed{0.7479} \)
