Answer
$P(X\lt75)=0.2327$
Work Step by Step
$μ_X=np=300\times0.267=80.1$
$σ_X=\sqrt {np(1-p)}=\sqrt {300\times0.267(1-0.267)}=7.66$
$P(X\lt75)=P(X\leq74)$
Let's find the z-score for 74.5:
$z=\frac{X-μ}{σ}=\frac{74.5-80.1}{7.66}=-0.73$
According to Table V, the area of the standard normal curve to the left of z-score equal to -0.73 is 0.2327
