Question

In which of the following situations would it be appropriate to use a normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?

a. n=10,p=0.9
b. n=100,p=0.01
c. n=50,p=0.5
d. n=30,p=0.8

Answer 1

Option c, where n=50 and p=0.5, is the scenario wherein a normal distribution best approximates the binomial distribution since np and nq values are sufficient for the approximation.

Step-by-step explanation:

The most appropriate case for using a normal distribution to approximate a binomial distribution is option c. n=50, p=0.5, because it best meets the criteria for a normal approximation.

A normal distribution can be used to approximate a binomial distribution when the number of trials (n) is large and the success probability (p) is neither very high nor very low.

The product of np and nq (where q=1-p) should be greater than five to ensure a close approximation. For option c, we have n = 50 and p = 0.5, which means np = 50 * 0.5 = 25 and nq = 50 * (1 - 0.5) = 25, both of which are greater than five and imply a symmetric distribution.

Other options either have too high a success probability (a, d) or too few trials (b) relative to the success probability for a reliable normal approximation to the binomial.