Question

1. Suppose X is binomial with p = .15. What does n have to be (at a minimum) to use the normal approximation for X?

2. Suppose X is binomial with p = .85. What does n have to be (at a minimum) to use the normal approximation for X?

3. Explain why the same n works for both of the previous problems.

Answer 1

Normal approximation to binomial can be applied when np 5 and nq 5

p = 0.15

If np = 5

n x 0.15 = 5

n = 33.33

q = 1 - p = 0.85

n x 0.85 = 5

n = 5.88

Take the larger of n values and round up

Sample size required = 34

When p = 0.85

np = 5

n = 5.88

q = 1 - 0.15

nq = 5

q = 33.33

Sample size required = 34

Because the probability values 0.15 and 0.85 are complement of each other, when one is p, the other one is q. Since both np and nq must be greater than 5, the same n works for both of the previous problems.