Chebyshev's Theorem

[taytay822]

The mean income of a group of sample observations is $500; the standard deviation is $40. According to Chebyshev's theorem, at least what percent of the incomes will lie between $400 and $600?

I tried the formula 1-1/k2 and I am not coming out with the right answer... please help

[stapel_eliz]

Please show your steps, so we can try to help you find any error(s). Also, please provide the book's answer. (It might be wrong!)

Thank you!

[taytay822]

I am doing an online assignment and whenever I typed in the answer it told me I had it incorrect. I received some help from a classmate, but I still don't know how they got the k or the std. dev

_
x ± k*s

1-1/k2

1-1/(2.5)2

1-1/6.25

=.84 or 84%

[stapel_eliz]

I still don't know how they got the k or the std. dev

You were given the standard deviation: 40.

The interval they gave you was one hundred to either side of the mean. How many standard deviations is this? (Hint: Divide 100 by 40.)

The number of standard deviations is the value of k.