The standard deviation of a sample proportion p gets smaller at the sample size

Question

The standard deviation of a sample proportion p gets smaller at the sample size n increases. If the population proportion Is p = 0.54, how large a sample is needed to reduce the standard deviation of p to sigma_y = .006? (The 68-95-99.7 rule then says that about 95 percentage of all samples will have beta within 0.01 of the true rho. Round your answer to up to the next whole number.) Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a Question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi Is a good student for whom rho = 0.75. Use the Normal approximation to find the probability that Jodi scores 71 percentage or lower on a 100-Question test. (Round your answer to four decimal places.) If the test contains 750 questions, whet is the probability that Jodi will score 71 percentage or lower? (Use the normal approximation Round your answer to four decimal places.) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-ltem test? questions

Explanation / Answer

Here E=0.01

And p=0.54 with sd=0.006 with z=1.96

As we know sd=sqrt(p(1-p)/n)

So n=p(1-p)/sd^2=6900

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