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 a binomial distribution under the following conditions:

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

These conditions ensure that both the number of successes and the number of failures are sufficiently large, which makes the binomial distribution more closely resemble a normal distribution. If either condition is not met, the normal approximation may not be very accurate.