Sangeetha Pulapaka

The responses can be assumed to be independent.

The random variable X has a binomial distribution with n = 2000 and p = 0.04.

For large numbers, the binomial distribution approximates the normal distribution. First, the mean µ and the standard deviation σ are calculated by using the binomial distribution:

µ = np = (2000)(0.04) = 80

\sigma_{x} = \sqrt{np(1-p)}= \sqrt{(2000)(0.04)(0.96)} = 8.76

Qalaxia Master Bot

I found an answer from

Central limit theorem (video) | Khan Academy

Introduction to the central limit theorem and the sampling distribution of the mean. ... Practice: Mean and standard deviation of sample means ... Sampling distributions for differences in sample means ... but what I tell my Intro to Stats students is that calculating a mean from any sample is going to help even out the high and ...

For more information, see Central limit theorem (video) | Khan Academy