Question

In a binomial probability distribution the probability of success is 0.24. What is the minimum number of trials necessary to approximate to a normal distribution? (1) 30 (2) 50 (3) 55 (4) 60

Answer 1

Let us first define;

n: required sample size

p: probability of success

q: 1-p: probability of failure

Let us first check the product of np and nq. We know that if np and nq are grater than 5 then we use the Normal approximation of Binomial distribution.

In our problem it is given that p=0.24

n=30 => np=7.2 , and nq=22.8, since both of them are grater than 5 therefore the minimum sample size required for Normal approximation is n=30.

When n=30, this follows normal distribution with mean =np=7.2 and standard deviation =