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This Java applet shows how the binomial distribution can be approximated by the normal distribution. The initial values are for a binomial distribution with the parameters N = 8 and p = 0.5 where N is the number of trials and p is the probability of success on each trial. You can change the values of N and p and see the result (Hit the enter or tab key after changing a value).
You can use this applet to calculate the probability of obtaining a given number of successes. For example, to calculate the probability of exactly 6 successes out of 8 trials with p = 0.50, enter 6 in both the "from" and "to" fields and hit the "Enter" key. The actual binomial probability is 0.1094 and the approximation based on the normal distribution is 0.1059. Note that the normal approximation computes the area between 5.5 and 6.5 since the probability of getting a value of exactly 6 in a continuous distribution is nil. Similarly, to approximate the probability of from 0 to 6 successes, you enter 0 in the "from" field and 6 in the "to" field. The area from below 6.5 is computed.