Consider a large population of scores from a negatively skew

Consider a large population of scores from a negatively skewed distribution with mean = 69 and standard deviation = 11. Imagine that you randomly selected a sample from that population that contained 45 scores. What is the PROBABILITY that the mean of the sample is above 64?

Solution

Mean ( u ) =69
Standard Deviation ( sd )=11
Number ( n ) = 45
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 64) = (64-69)/11/ Sqrt ( 45 )
= -5/1.64= -3.0492
= P ( Z >-3.0492) From Standard Normal Table
= 0.9989