suppose a fictitious national test is taken by 20 year olds

suppose a fictitious national test is taken by 20 year olds yearly and the national data says that the average score is 50 with a standard deviation of 5. We conduct the following experiment:

Solution

since sample is taken from a populatio with mean 50 and standerd deviation 5

hence mean of sample =50

and sum of scores =5000

variance of W=25

variance of Y=25