Answer
$P(X \geq 80) = 0.5517$
Work Step by Step
Here we have: n = 100, p = 0.80, x = 80
Check whether the normal distribution can be used as an approximation for the binomial distribution:
$np(1-p) = 100 x 0.80 (1 - 0.80) = 16 \gt 10$
Hence, the normal distribution can be used.
$μ_{x} = np = 100 \times 0.80 = 80$
$σ_{x} = \sqrt {np(1-p)} = \sqrt {80(.20)} = 4$
After applying the continuity correction, we have:
$z = \frac{x - μ_{x}}{σ_{x}} = \frac{79.5 - 80}{4} = -0.125$
$P(X \geq 80) = P(z > -0.125) = P(z < 0.125) = 0.5517$
