Question

1. Based on past experience, a bank believes that 7% of the people who receive loans will not make payments on time. The bank takes a random sample of 200 recently approved loans.

   1. Check the conditions for the Central Limit Theorem.

   2. Sketch and label the distribution of the sample proportion, p. Include the mean and 3 standard deviations from the mean.

   3. What is the probability that more than 10% of these clients will not make timely payments?

   4. Find the probability that between 5% and 10% of these clients will not make timely payments.

   5. What is the 90th percentile of the sample proportions of clients who will not make timely payments.

   6. Find the quartiles of the sample proportions of clients who will not make timely payments.

   7. What values of sample proportions of clients who will not make timely payments would be unusual? Explain.

   8. Construct and interpret a 95% confidence interval for the true proportion of clients who will not make timely payments.

   9. Since the U.S. economy has changed, bank officials would like to do a new study to estimate the true proportion of clients who will not make timely payments. Assume you have no preconceived idea of what that proportion would be. What sample size is needed if you wish to be 99% confident that your estimate is within 2% of the true proportion.   

   10. Based on previous research, you assume the proportion of clients who will not make timely payments is 7%. What sample size is needed if you wish to be 99% confident that your estimate is within 2% of the true proportion.

Answer 1

With mean 0.07 and 3 SD below mean value at 0.016 and 3SD above mean at 0.124

Posted the first 5 parts of the sum.

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