Assume the portfolio returns for a large population of large cap equity funds has a standard deviation of 8.1 %, and returns are independent across funds. If you are collecting a random sample of fund returns and want the standard deviation of sample mean distribution to be at most 1.7 %, what is the size of the sample you must collect?

Enter answer as the smallest integer sample that will accomplish your objective.

You want to construct a 95% confidence interval for the performance of a large population of mutual funds. Assume returns are independent across funds, and the standard deviation of fund returns is 9.8 %. If you want the width of your interval to be 2.3 %, what sample size must you collect?

Assume sample is large enough that the sample mean is normally distributed.

Enter answer as the smallest integer sample that will accomplish your objective.

A portfolio's annual returns are normally distributed with a mean of 10 % and a standard deviation of 22 %. Over the past 6 years, you observe an average annual return of -3 %. What is the probability of observing an average annual return over 6 years of -3 % or less?

Enter answer in percents, accurate to 2 decimal places.

You collect a small sample of 20 fund returns, which turns out to have a sample mean of 10 % and a sample standard deviation of 7 %. Assuming fund returns are normally distributed, what is the lower bound of the 95% confidence interval for fund returns?

Enter answer in percents, accurate to two decimal places.

A mutual fund manager is trying to estimate the expected fund flows for the next quarter. To make the estimate, the manager calls 15 clients and asks each of them about their planned deposits/withdrawals from the fund. The asset-weighted average of the sample is a 2.3 % change in assets under management, with a standard deviation of 13 %. What is the width of the 95% confidence interval for next quarter's fund flows?

Enter answer in percents, accurate to two decimal places.