Question

With binomial data, using the information below, what is the value of the Condition to use the normal approximation?

n=30:p=0.15

Answer 1

To use the normal approximation, both np and nq must be greater than five. In this case, np = 4.5, which does not meet the condition, so the normal approximation should not be used for a binomial distribution with n=30 and p=0.15.

Step-by-step explanation:

To determine if we can use the normal approximation to the binomial distribution, we have to check if our example meets the condition np > 5 and nq > 5. Here, we have n = 30 and p = 0.15.

Let's calculate np and nq:

• np = 30 × 0.15 = 4.5
• q = 1 - p = 1 - 0.15 = 0.85
• nq = 30 × 0.85 = 25.5

Since np is not greater than 5 (np = 4.5), the condition to use the normal approximation is not met. Thus, we should not use the normal approximation for this binomial distribution.