There are three brands of milk for sale in a supermarket. Let's call them brand A, B, and C. A customer who purchases milk will choose brands A,B, and C with probability 0.6, 0.3, 0.1, respectively. Each day, the toal number of customers who purchase milk at this market follow a Binomial(200,0.5) distribution. Let X be the daily number of sales of brand A milk. Find E(X) and V(X)

Answer 1

Since n = 200, .6 = 120, .3 = 60, and .1 = 20

Therefore, the expected vale of X is:
E(X) = sum x*p = 120(.6) + 60(.3) + 20(.1) = 92

To get the variance, subtract the mean (expected value) from each X. Next, square each of those values. Finally, add the squares times their respective probabilities. If you need the standard deviation, just take the square root of the variance. That should be it.

Answer 2

In a batch of 1000 cartons estimate the number of cartons that contain less than the number of cartons that contain less the advertised volume of milk