The average annual return over the period 1926-2009 for small stocks is 21.2%, and the standard
deviation of returns is 21.2%. Based on these numbers, what is a 95% confidence interval for
2010 returns?
A) -10.6%, 31.8%
B) 0%, 42.4%
C) -21.2%, 42.4%
D) -21.2%, 63.6%

Hi, the empirical rule dictates that 95% of the data is found within +/- 2 standard deviations from the mean, therefore our interval can be found doing the following calculations.

[tex]L.Limit=Mean-2(S.D)[/tex]

That is:

[tex]L.Limit=0.212-2(0.212)=-0.212[/tex]

Now, the higher limit.

[tex]H.Limit=Mean+2(S.D)[/tex]

[tex]H.Limit=0.212+2*(0.212)=0.636[/tex]

So, the answer is D) -21.2%, 63.6%

Best of luck.

The average annual return over the period 1926-2009 for small stocks is 21.2%, and the standard deviation of returns is 21.2%. Based on these numbers, what is a 95% confidence interval for 2010 returns? A) -10.6%, 31.8% B) 0%, 42.4% C) -21.2%, 42.4% D) -21.2%, 63.6%

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The average annual return over the period 1926-2009 for small stocks is 21.2%, and the standard
deviation of returns is 21.2%. Based on these numbers, what is a 95% confidence interval for
2010 returns?
A) -10.6%, 31.8%
B) 0%, 42.4%
C) -21.2%, 42.4%
D) -21.2%, 63.6%