The GPAs of all students enrolled at a large university have

The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29. Find the probability that the mean GPA of a random sample of 20 students selected from this university is

2.90 or lower

Solution

Normal Distribution
Mean ( u ) =3.02
Standard Deviation ( sd )=0.29
Number ( n ) = 20
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 2.9)         = (2.9-3.02)/0.29/ Sqrt ( 20 )
= -0.12/0.065= -1.8505
= P ( Z >-1.8505) From Standard Normal Table
= 0.9679                  
P(X < = 2.9) = (1 - P(X > 2.9)
= 1 - 0.9679 = 0.0321