Final answer:
To find the probability that between 37 and 437 of the sampled ads worked during summer vacation, use the normal distribution. To find the probability that over 35% of the ads worked, use the normal approximation to the binomial distribution or a calculator.
Step-by-step explanation:
To find the probability that between 37 and 437 of the sampled ads worked during summer vacation, we need to use the normal distribution. We can standardize the values using the z-score formula, which is z = (x - μ) / σ. We then use a standard normal distribution table or a calculator to find the probabilities.
The probability that between 37 and 437 ads worked can be calculated as P(37 ≤ X ≤ 437) = P(X ≤ 437) - P(X ≤ 36). The probabilities can be found using the z-scores for each value, and then subtracting the cumulative probabilities from each other.
To find the probability that over 35% of the ads worked, we can use the normal approximation to the binomial distribution or a calculator to find the probability of getting more than a certain number of successes. We can calculate it as 1 - P(X ≤ np - 1.96 * √(np(1-p))), where n is the sample size, p is the probability of success, and 1.96 is the z-value associated with a 95% confidence level.