Always skip a space after <  when you post on here, 
otherwise the computer will thinks it's an HTML tag 
and will delete it.  So what you wrote came out
garbled.

For P( lower number < Z < upper number )

If you want P(Z < a), the lower number is -99999999
If you want P(Z > a), the upper number is 99999999.

On your TI-84, press 2ND then VARS then 2. You see this screen

    normalcdf
lower:        <--put in the lower number
upper:        <--put in the upper number
μ:         <--put in the mean, which is 0 for standard normal
σ:      <--put in the standard deviation, which is 1 for std. normal
Paste         <--highlight this and press ENTER

You'll see this on the screen:

normalcdf(1.19,2,0,1)  if you wanted this P(1.19 < Z < 2)

Press ENTER and read 0.094273194

Edwin