Answer
$P(X = 50) = \frac{100!}{50!(100-50)!} \times 0.05^{50} \times (1 - 0.05)^{(100-50)}= 6.9 \times 10^{-38}$
The normal distribution can not be used.
Work Step by Step
Here we have: n = 100, p = 0.05, x = 50
Using the binomial probability formula:
$P(X = 50) = \frac{100!}{50!(100-50)!} \times 0.05^{50} \times (1 - 0.05)^{(100-50)}$
$= 6.9 \times 10^{-38}$
Check whether the normal distribution can be used as an approximation for the binomial distribution:
$np(1-p) = 100 \times 0.05 (1 - 0.05) = 4.75 \lt 10$
Hence, the normal distribution can not be used.
