Question

Uncle Henry has been having trouble keeping his weight constant. In fact, during each week, his weight changes from the beginning of the week to the end of the week by a random amount, uniformly distributed between -0.5 and 0.5 pounds. Assuming that his weight change during any given week is independent of his weight change during any other week, approximate the probability that at the end of 50 weeks Uncle Henry will have had a net change in weight of at least +3 pounds. You may want to refer to the standard normal table .

Answer 1

The answer can be calculated by Central Limit Theorem.
You need to find P(sn=>3) where sn= x1+x2+....+xn. So, to approximate this sum, we just need to calculate P(zn=>z) where zn=sn/(n^1/2)*standard deviation, and z= 3/2.0364. Finally, because we are dealing with the CDF of a normal random variable, we should calculate 1-P(zn<3/2.0364) by looking at standard normal table. The final answer is 0.0708.