00:01
For this question, in a sample of 1 ,024 mutual funds, the mean one -year return is 6 .10, and the standard deviation is 0 .75.
00:15
For part a, we're asked, according to the empirical rule, what percentage of these funds is expected to be within plus or minus three standard deviations of the mean? the empirical rule tells us that 99 .7 % of a distribution that is approximately bell -shaped is within three standard deviations of the mean.
00:37
The mean.
00:39
So if we can assume that the distribution of the mutual funds is bell -shaped, then the answer is 99 .7%.
00:52
And then according to shebyshev rule, what percentage of these funds are expected to be within three standard deviations of the mean? shebyshev's rule says at least 1 minus 1 over k squared percent of a distribution is within k -standard deviations of the mean.
01:29
So here, k is equal to three because you want to know how much of the distribution is within three standard deviations of the mean.
01:47
And this comes out to 88 .89%.
01:54
Actually, this should not be a percent sign here.
01:57
This is the proportion.
02:00
We have to multiply by 100 to give it in percent.
02:06
So the answer for b, it should be at least 88 .89%...