Question

According to the Chebyshev rule, at least 96% of these funds are expected to have one year total returns between what two amounts?

Answer 1

what is your mean and std dev?

Answer 2

.96 = (1 - 1/k^2)

solve for k to get the number of std. devs. then you need to be with that many std. devs of the mean so you'll have to convert.

Answer 3

The mean is 7.30 and the sd is 3.50
I would like someone to break it down for me mathematically

Answer 4

i did... do you understand chebyshevs inequality and what it means?

Answer 5

i do not :(

Answer 6

ok so, i calculated the percentage of the funds are expected to be within a +/-6 standard deviation of the meant to be 97.22%
Then it asks me - at least 93.75% of these funds are expected to have one year total returns between what two amounts?
How do i calculate that, please?

Answer 7

what chebyshev's theorem says is that no matter what the distribution of you data is, there is at least (1-1/k^2)% of the data within k standard deviations of the mean.

so, let's say you have a mean of 7.30 and a standard deviation of 3.50, just like your problem. so how much of the data must be within 2 standard deviations?

well, we use chebyshev's to calculate:

\[1-\frac{ 1 }{ 2^2 }=1-\frac{ 1 }{ 4 }= \frac{ 3 }{ 4 }=75%\]

we can use it in reverse too! say we want to know how many deviations are needed to contain 96% of our data (just like your problem).

then we set up and solve for k:

\[96\%=.96=1-\frac{ 1 }{ k^2 } \Rightarrow \frac{ 1 }{ k^2 }=.04 \Rightarrow k^2 = 25 \Rightarrow k = 5\]

how are you up to here?

Answer 8

and that should be 75%

Answer 9

the 75 should be 75%

Answer 10

so now that you know how many standard deviations, you just need to figure out what that is in terms of the data...


mean + 5 std. devs => 7.30 +5*3.50 = ? (upper limit)
mean - 5 std. devs => 7.30 -5*3.50 = ? (lower limit)

Answer 11

So upper limit is 43.05 and lower is 8.05?