A population has a mean of 50 and a standard deviation of 12

A population has a mean of 50 and a standard deviation of 12. A sample of size 144 observations is drawn from the population. What is the probability that the sample mean will be less than 52?

Mean ( u ) =50
Standard Deviation ( sd )=12
Number ( n ) = 144
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)
P(X < 52) = (52-50)/12/ Sqrt ( 144 )
= 2/1= 2
= P ( Z <2) From Standard NOrmal Table
= 0.977