Finding x where P(-X < x-5 < X) = 0.99 with normal distribution

[sisyphus0321]

Homework Statement

Assume x is normally distributed with a mean of 5 and standard deviation of 4. Determine value of x that solves:
P(-X<x-5<X) = .99

Homework Equations

I have been using normalCDF and inverse functions on the TI-84 to solve, and I understand how to do these without the calc as well using the standard (x-mean)/stand dev techniques.

The Attempt at a Solution

I have a good understanding of how to work the general problems as this is the last one out of 50 I have solved. The issue is how to start this one? The teacher left a mysterious hint: Distribution?

 

[Mark44]

Homework Statement

Assume x is normally distributed with a mean of 5 and standard deviation of 4. Determine value of x that solves:
P(-X<x-5<X) = .99

From the probability above, what you want to solve for is X, not x.

Homework Equations

I have been using normalCDF and inverse functions on the TI-84 to solve, and I understand how to do these without the calc as well using the standard (x-mean)/stand dev techniques.

The Attempt at a Solution

I have a good understanding of how to work the general problems as this is the last one out of 50 I have solved. The issue is how to start this one? The teacher left a mysterious hint: Distribution?

You know that your random variable X is n(5, 4). If you let Y = X - 5, how is Y distributed? What would you need to do to get a probability involving Z, the standard normal n(0, 1) random variable? How should your original probability be rewritten so that it involves Z (and from which you can get the values you need from a table or maybe your TI?