Question

Can you use a normal distribution to approximate the binomial distribution? If yes, find the mean and standard deviation. If not, explain why.

A. Yes, the mean is 35 and the standard deviation is 5.4.

B. No, because the sample size is too small.

C. Yes, the mean is 28.35 and the standard deviation is 4.27.

D. No, because the probability of success is not provided.

Answer 1

Yes, you can use a normal distribution to approximate the binomial distribution under certain conditions.

Step-by-step explanation:

Yes, you can use a normal distribution to approximate the binomial distribution under certain conditions. This is known as the normal approximation to the binomial distribution. The conditions for a successful approximation are:

1. The number of trials, denoted as n, should be large (typically greater than 30).
2. The probability of success, denoted as p, should be moderate (between 0.1 and 0.9).
3. The sample size, denoted as np, should also be moderate (between 5 and 20).

If these conditions are met, you can use the mean and standard deviation of the binomial distribution to approximate a normal distribution. The mean of the normal distribution is given by μ = np and the standard deviation is given by σ = √np(1-p).

So, for the given question, we cannot confirm the answer options without knowing the values of n and p.