Answer
$P(X \geq 20) = 0.1190$
Work Step by Step
Here we have: n = 500, p = 0.03, $x \geq 20$
Check whether the normal distribution can be used as an approximation for the binomial distribution:
$np(1-p) = 500 x 0.03 (1 - 0.03) = 14.55 \gt 10$
Hence, the normal distribution can be used.
$μ_{x} = np = 500 \times 0.03 = 15$
$σ_{x} = \sqrt {np(1-p)} = \sqrt {15 (0.97)} = 3.81$
$z = \frac{x - μ_{x}}{σ_{x}} = \frac{19.5 - 15}{3.81} = 1.18$
$P(X \geq 20) = P(z > 1.18) = 0.1190$
