Question

For a sample size of n=26 and a population parameter of p=0.4, a normal curve can be used to approximate the binomial probability histogram.

True or false?

Answer 1

False - for a normal approximation to the binomial distribution, the sample size (n) > 25 and the product of the sample size and the population proportion < 5 (i.e. np < 5). This is known as the Central Limit Theorem. In this case, although n > 25, np = 26 * 0.4 = 10.4 > 5, hence the CLT cannot be used in this context.