A binomial distribution with n number of trials, and probability of success p can be approximated well by a normal distribution with mean np and variance if np 5 and n(1-p) 5.

Question

A binomial distribution with n number of trials, and probability of success p can be approximated well by a normal distribution with mean np and variance  if np > 5 and n(1-p) > 5.

Quizplus · Accepted Answer

This is a well-known approximation called the normal approximation to the binomial distribution. The condition np > 5 and n(1-p) > 5 ensures that the binomial distribution is not too skewed and the normal approximation is accurate. The mean of the normal distribution is np and the variance is np(1-p). However, there is a typo in the given variance, it should be np(1-p) instead of 11eb06d9_cc36_1b7f_8177_b1ed5a4d7392_TB1387_11.

A Binomial Distribution with N Number of Trials, and Probability