[Question]How to find lower bound for this exercise

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To find the lower bound for the probability that the difference between the relative frequency p^ and p is less than 0.01 with n = 4500, the Central Limit Theorem can be applied. The discussion emphasizes the need to identify appropriate values for p^ and p, with a focus on calculating the corresponding Z-score (Za/2) for the specified difference. It suggests that understanding the Central Limit Theorem is crucial for solving the problem effectively. The lack of a confidence interval in the exercise raises questions about the methods available for determining the lower bound. Overall, applying statistical principles and the Central Limit Theorem is essential for finding the solution.
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Homework Statement



Apply the Central limit theorem to evaluate approximately the lower bound for the probability that the difference between the relative frequency p^ and p is less than 0.01, if n = 4500

Homework Equations



This exercise do not give me the confidence interval? What function can help me solve this problem

The Attempt at a Solution


I think in this problem, i will choose random p^, p and the different between them is 0.01 => find approximately Za/2 => i have lower bound
 
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It would be a good idea to start by stating the "central limit theorem". That might give you some ideas.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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