When n is reasonably large and p isn't too close to 0 or 1,the binomial distribution can be well approximated by which of the following distributions
A) Uniform distribution
B) Normal distribution
C) Triangular distribution
D) None of these options

Question

When n is reasonably large and p isn't too close to 0 or 1,the binomial distribution can be well approximated by which of the following distributions
A) Uniform distribution 
B) Normal distribution 
C) Triangular distribution 
D) None of these options

Quizplus · Accepted Answer

When n is reasonably large (greater than 30) and p is not too close to 0 or 1 (p should be between 0.05 and 0.95), the binomial distribution can be approximated by the normal distribution. This is known as the normal approximation to the binomial distribution. The mean of the normal distribution is np and the standard deviation is sqrt(np(1-p)). This approximation can be used for calculating probabilities and making statistical inferences. Therefore, B) Normal distribution is the best choice for approximating the binomial distribution under the given conditions.

When N Is Reasonably Large and P Isn't Too Close