Final answer:
To find the probability that exactly 48 out of 198 eligible voters aged 18-24 voted, we can use a normal approximation. The probability of exactly 48 voters is approximately 0.2266, or 22.66%.
Step-by-step explanation:
To find the probability that exactly 48 out of 198 eligible voters aged 18-24 voted, we can use a normal approximation. We know that 22% of eligible voters aged 18-24 voted based on a previous study. The first step is to calculate the mean and standard deviation for a binomial distribution, where n is the number of trials and p is the probability of success.
Mean (μ) = n * p = 198 * 0.22 = 43.56
Standard Deviation (σ) = sqrt(n * p * (1-p)) = sqrt(198 * 0.22 * 0.78) = 5.98
Next, we use the normal approximation to find the probability of exactly 48 voters. We calculate the z-score using the formula z = (x - μ) / σ, where x is the number of voters. For 48 voters:
z = (48 - 43.56) / 5.98 = 0.7563
We can then use a standard normal distribution table or a calculator to find the corresponding probability. The probability of exactly 48 voters is approximately 0.2266, or 22.66%.