Verified answer

z = ( x - μ ) / σ

P ( x < 165) = P ( z < 1 ) = 0.841344681

0.841344681 - 0.4505= 0.390844681

P ( x < 145.843227292 ) = P ( z < -0.277118181) = 0.390844681

x0 = 145.843227292

P (145.843227292 < x < 165) = P (-0.277118181 < z < 1) = 0.4505