Answer
$P(X \geq 110) = 0.0066$
Work Step by Step
Here we have: n = 200, p = 0.46, $x = \geq 110$
Using the binomial probability formula:
Check whether the normal distribution can be used as an approximation for the binomial distribution:
$np(1-p) = 200 x 0.46 (1 - 0.46) = 49.68 \gt 10$
Hence, the normal distribution can be used.
$μ_{x} = np = 200 \times 0.46 = 92$
$σ_{x} = \sqrt {np(1-p)} = \sqrt {92 (0.54)} = 7.05$
Applying continuity correction, we have:
$z = \frac{x - μ_{x}}{σ_{x}} = \frac{109.5 - 92}{7.05} = 2.48$
$P(X \geq 109.5) = P(z > 2.48) = 0.0066$
