Let X be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the number of trials (n) ?

Step-by-step solution

Let n be the number of trials, p be the probability of success, and q be the probability of failure. Given mean = np = 200 Given variance = npq = 160 Dividing variance by mean: npq np = 160 200 q = 4 5 Since p + q = 1 , we have p = 1 - 4 5 = 1 5 Substituting the value of p in the mean equation: n 1 5 = 200 n = 1000