Answer
$P(X \leq 30) = P(z < -3.09) = 0.0010$
Work Step by Step
Here we have: n = 250, p = 0.2, $x \leq 30$
Check whether the normal distribution can be used as an approximation for the binomial distribution:
np(1-p) = 250 x 0.2 (1 - 0.2) = 40 > 10
Hence, the normal distribution can be used.
$μ_{x} = np = 250 \times 0.2 = 50$
$σ_{x} = \sqrt {np(1-p)} = \sqrt {50 (0.8)} = 6.32$
$z = \frac{x - μ_{x}}{σ_{x}} = \frac{30.5 - 50}{6.32} = -3.09$
$P(X \leq 30) = P(z < -3.09) = 0.0010$
