Answer
$P(X\geq75)=0.0007$
Work Step by Step
37% = 0.37
$μ_X=np=150\times0.37=55.5$
$σ_X=\sqrt {np(1-p)}=\sqrt {150\times0.37(1-0.37)}=5.91$
Let's find the z-score for 74.5:
$z=\frac{X-μ}{σ}=\frac{74.5-55.5}{5.91}=3.21$
According to Table V, the area of the standard normal curve to the left of the z-score equal to 3.21 is 0.9993.
But, we want the area of the standard normal curve to the right (at least 75) of the z-score equal to 0.9993:
$1-0.9993=0.0007$
