Suppose we take a random sample X1X100 of size 100 from a po

Suppose we take a random sample X_1,...,X_100 of size 100 from a population having expected value 5 and variance 25. What is the approximate probability that the sample mean X exceeds 6? What result did you rely on to find this probability?

Solution

Mean ( u ) =5
Standard Deviation ( sd )=5
Number ( n ) = 100
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 6) = (6-5)/5/ Sqrt ( 100 )
= 1/0.5= 2
= P ( Z >2) From Standard Normal Table
= 0.0228