00:01
Hey there, welcome to numerade.
00:04
We are looking at the one -year total percentage return of mutual funds, giving us a population mean here that equals around 8 .3 and a population standard deviation here that equals around 2 .5.
00:21
So we have 8 .3 and 2 .5, and we're working on part c.
00:27
Asking, based on chebyshev's rule, which is 1 minus 1, divided by k square, where k represents the number of standard deviations away from the mean.
00:46
So we're asked to use chebyshev's rule in order to determine that at least 96 % of these funds are expected to have one -year total returns between these two amounts.
00:59
So therefore what we have here is basically 1 minus 1 divided by k square will equal the 0 .96.
01:11
So with this we are going to be subtracting 1 given us double negative so 1 divided by k squared equaling so this is minus 1 so this will be 0 .04.
01:25
So with this we have to move our values k square to the right.
01:33
Us basically k squared equals 1 divided by 0 .04 in which we can just take the square root given us k equals let's see what we get let's do 1 divided by 0 .04 first and then square root of doubt is just 5 so we get k equals 5 okay so let me just convert this back to black here so since k equals 5, we can find the two amounts here in which we have our x low and x high.
02:18
So for x low, we are going to be taking the negative k, negative 5, and high is positive 5 times 2 .5 for both and then plus our mean, which is the 8 .3...