Reading 10 Practice Problem 2

CFA Level I Quant
#1

Hi

I am confused on the answer for Q2 part A.

The Question:

Petra Munzi wants to know how value managers performed last year. Munzi
estimates that the population cross- sectional standard deviation of value manager returns is 4 percent and assumes that the returns are independent across
managers.
A. Munzi wants to build a 95 percent confidence interval for the mean return.
How large a random sample does Munzi need if she wants the 95 percent
confidence interval to have a total width of 1 percent?

The Answer:

image
image1013×412 105 KB

I am confused as to how they arrived at the highlighted formula?

Could someone please explain this to me?

Thank you.

#2

This is equivalent to the right end of the interval minus the left end of the interval, which is equal to the length of the interval. The sample mean will be exactly in the middle of this interval.

1 Like
#3

The left side of the equation is the width of a 95% confidence interval. The right side is 1%. Munzi wants the former to equal the latter.

1 Like
#4

It’s that simple?? Yeah I was overcomplicating this haha.

Thank you for your response!

#5

Thank you! I was over complicating this.

#6

It is.

My pleasure.