Answer
$P(X = 30) = \frac{40!}{30!(40-30)!} \times 0.25^{30} \times (1 - 0.25)^{(40-30)}$
= 0.0001
The normal distribution can not be used.
Work Step by Step
Here we have: n = 40, p = 0.25, x = 30
Using the binomial probability formula:
$P(X = 30) = \frac{40!}{30!(40-30)!} \times 0.25^{30} \times (1 - 0.25)^{(40-30)}$
= 0.0001
Check whether the normal distribution can be used as an approximation for the binomial distribution:
$np(1-p) = 40 \times 0.25 (1 - 0.25) = 7.5 \lt 10$
Hence, the normal distribution can not be used.
