Chebyshev’s inequality problem in one exercises I can't understand if I did it right or not This is what do I have to solve:
Byron Book: Exercise 8.3 chapter 8
Verify the use of Chebyshev’s inequality in (8.6) of Example 8.16. Show that if the population
mean is indeed 48.2333 and the population standard deviation is indeed 26.5170, then at
least 8/9 of all tasks require less than 127.78 seconds of CPU time.
This is how I did it :
So first I calculated: 127.78-48.23 = 79.5
Then I wrote P(X&lt;127) &lt; (26.5^2)/(79.5^2) = 0.11
I don't understand if I did it right because I did not use this part : at least 8/9 of... and I think it is important.
Can anyone help me with this ? Thank you in advance.
The exercise above is right but is missing something. You need to do 1-0.11 since you need to find the &lt;, not the &gt;. When I wrote 0.11 I have found the &gt; but I need the &lt; so  1-.. .