You're looking for [tex]k[/tex] such that
[tex]\mathbb P(Z<k)=0.90[/tex]
A z-score table or any calculator with an inverse CDF functionality gives an answer of about
[tex]k\approx1.2816[/tex]
For example, on a TI-83 calculator, you would use
invNorm(.90)
or
invNorm(.90, 0, 1)
