Question

Binomial probability distributions depend on the number of trials n of a binomial experiment and the probability of success p on each trial. Under what conditions is it appropriate to use a normal approximation to the binomial? (Select all that apply.)
np > 5 p < 0.5 p > 0.5 nq > 5 np > 10 nq > 10

Answer 1

Answer:

a) np > 5

d) nq > 5

Step-by-step explanation:

Binomial probability distributions depend on the number of trials n of a binomial experiment and the probability of success p on each trial.

A binomial distribution can be approximated with the help of normal distribution.

A binomial distribution has parameters:

$X \sim B(n,p)$

where n is the number of independent trials and p is the probability of success.

If p is the probability of success, then we define probability of failure as:

$q = 1-p$

A normal distribution can be used to approximate the binomial distribution if

$np > 5\\nq = n(1-p) > 5$

Thus, the correct answer is

a) np > 5

d) nq > 5