Find 'k' (# of standard deviations from the mean)

[rogo0034]

Homework Statement

μ=10 σ^2=4

I seem to be getting the first two just time the same as i get every other problem, but I can't seem to get C)'s 'k'. typically i will take the absolute value of the portion that we are looking at, i.e. P(-10<X<10) would be |-10+10| = 20, divide that by two to get the center, 20/2 = 10 and then divide that by the standard deviation, which for this problem is 2. So 10/2 = 5, which i use for K. It's worked for every problem so far, but for C) they have 2.5 instead of (5/4) that i get. Any ideas?

Homework Equations

P(μ−kσ<X<μ+kσ)≥1− 1/k^2

The Attempt at a Solution

 

[kurt.physics]

A) P(X<10) = P(X≤10) = P(X<μ+kσ) = P(X<10+kσ) = P(μ−kσ<X<μ+kσ) B) P(X>10) = P(X≥10) = P(X>μ+kσ) = P(X>10+kσ) = P(μ−kσ<X<μ+kσ)C) P(−10<X<10) = P(X>−10) & P(X<10) = P(X>μ−kσ) & P(X<μ+kσ) = P(μ−kσ<X<μ+kσ)