Errm.
If we split up the interval for X into 2 disjoint intervals we get:
Pr(1 ≤ X ≤ 19) = Pr((1 ≤ X ≤ 17) ∨ (17 < X ≤ 19))
Application of the sum rule for disjoint events gives us:
Pr((1 ≤ X ≤ 17) ∨ (17 < X ≤ 19)) = Pr(1 ≤ X ≤ 17) + P(17 < X ≤ 19)
So Pr(1 ≤ X ≤ 19) ≥ Pr(1 ≤ X ≤ 17).
I'm just a little lost in the question I think.
So we did a two tailed inequality and got 0.86.
Then a one tailed version to get 0.80.
Now are we trying to find the final answer? Can you explain why 0.80 is not the answer? Isn't that what the question is asking for?
I don't understand what you mean when you say 'highest minimum value'.
Thanks for helping me and im sorry for being tough.
0.80 is a correct answer and so is 0.86.
Since Chebyshev gives an upper estimate of the tails and the upper estimate of 0.14 for the tails is sharper than the upper estimate of 0.20.
This means that 0.86 is a better answer, although 0.80 is also a correct answer.
Cool, this is the closest I came, my reasoning was that 0.14 < 0.20 so 0.86 is the answer to use, is that some what a correct thought process or have I come to the correct conclusion by chance?
Not sure what you mean by tails you see.
EDIT: Oh no I do know what tails are.........