As observed from the reading, large samples of a binomial distribution seem to exhibit characteristics of a normal distribution. This paper intends to explore this discovery and investigate available literature regarding this phenomenon.It is important to recall that the binomial event is one wherein only two possible outcomes make up the probability space. Hence, either one or the other may occur.
Repeated binomial experiments reveal that the number of possible outcomes increase by powers of 2. For example, tossing a coin thrice creates 8 possible outcomes. The binomial probability distribution describes the likelihood of certain numbers of successes occurring from a specified sample (Tijms 201). As the sample increases, there is less likelihood of there being too many or too few successes and the bulk of the distribution falls in the middle where there are an average number of successes.This attribute of the binomial distribution is primarily what makes the approximation to a normal distribution feasible. Like the normal distribution, a binomial distribution’s successes would have central tendencies and equal deteriorating likelihood going to either side of the center (205).
When the samples become large, the gradually increasing number of steps on each direction showing decreasing point-probabilities models a normal curve. From the discreet binomial distribution, the normal approximation is made by connecting each data point with the next proceeding in both directions. If the sample is small, this creates a crude approximation as there is too much distance between one data point and the next. However as the sample becomes larger, more data points “fill-in” the gaps between the previous data points making the distances shorter and thereby making the approximation more accurate (206).In conclusion, the binomial distribution can be approximated using a normal distribution because the fundamental nature of the binomial experiment follows the assumptions of central tendency made by the normal curve.Work CitedTijms, H. Understanding Probability. Cambridge Univ.