At LSU the mean age of the students is 223 years and the sta

At LSU, the mean age of the students is 22.3 years, and the standard deviation is 4 years. A random sample of 64 students is drawn. What is the probability that the average age of these 64 students is greater than 23 years?

Solution

Normal Distribution
Mean ( u ) =22.3
Standard Deviation ( sd )=4
Number ( n ) = 64
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 23)         = (23-22.3)/4/ Sqrt ( 64 )
= 0.7/0.5= 1.4
= P ( Z >1.4) From Standard Normal Table
= 0.0808