Question

We can use normal distribution as an approximation of a binomial distribution if

np≥

n(1-p)≥

(n - number of trials; p - probability of success)

Otherwise, the approximation is not very accurate.

Answer 1

The normal distribution can be used as an approximation of the binomial distribution when both of the following conditions are satisfied:

1. \( np \geq 10 \)
2. \( n(1 - p) \geq 10 \)

Here, \( n \) is the number of trials and \( p \) is the probability of success. If both of these conditions are met, the binomial distribution can be approximated by a normal distribution, making calculations easier, especially for large \( n \). If either condition is not met, the normal approximation may not be accurate.