Answer:
[tex]X_{1}=1.23[/tex]
Explanation:
Given :
μ = 0
σ = 1
For 89th percentile
using invariant norm ( area, μ, σ )
    = inv. norm ( 0.89, 0, 1 )
    = 1.23
or
P ( x > [tex]X_{1}[/tex] ) = 0.89
[tex]P\left ( \frac{X-N}{\sigma } >\frac{X_{1}-0}{1}\right )=0.89[/tex]
[tex]P\left ( Z>Z_{1} )=0.89[/tex]
Now using Normal table, Z = 1.23
Therefore, [tex]\frac{X_{1}-0}{1}=1.23[/tex]
[tex]X_{1}=1.23[/tex]
