Is the normal distribution used to approximate a binomial probability distributi

Question

Is the normal distribution used to approximate a binomial probability distribution when n is small or large? Why?

Choose the correct answer below.

A.

When n is large because a binomial random variable can assume a large number of values, and the calculation of its probabilities can become tedious.

B.

When n is small because the probabilities of a binomial random variable can only be calculated by using a normal approximation.

C.

When n is large because the probabilities of a binomial random variable can only be calculated by using a normal approximation.

D.

When n is small because a binomial random variable can assume a large number of values, and the calculation of its probabilities can become tedious.

Explanation / Answer

Yes, the normal distribution used to approximate a binomial probability distribution when n is large.

Generally we do normal approximation to binomial if n is large and probability of success is closer to 0.5.

Thus, np >=5 and nq >=5

and we go for normal approximation because when n is large then calculation of probability using Binomial is dedious.

Therefore,

Answer: A) When n is large because a binomial random variable can assume a large number of values, and the calculation of its probabilities can become tedious.

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