There is a problem (the solution should use limit probability statements): One medical company invented some pills that should accelerate the growth of hair. The company wanted to try the pills on people - and so 2 groups of volunteers (each had 100 persons) were chosen to participate in the test. Persons in 1st group didn't take the pills and the experts noticed that the average monthly increment of the length of their hair was 3,5 cm, person in the 2nd group took the pills and the experts found out that the average monthly increment was 3,9 cm. It's known that the diffusibility (denoted D(X) for random variable X) of monthly increment of the length of hair is 0,5 cm^2. It was only a luck or the pills are really effective? What is the probability that by using the pills the hair will grow faster? I would like to know, how to use the limit statements from the probability theory (as Central Limit Statement, the Rule of Great Numbers...) on this problem. I know that it isn't so difficult, but this is new for me and I'm not able to applicate it yet. Thank you very much for help.