The College Student Journal Dcc 1992 investigated difference

The College Student Journal (Dcc. 1992) investigated differences in traditional and nontraditional students, where nontraditional students arc generally defined as those 25 years or older and who arc working full or part-time. Based on the study results, we can assume that the population mean and standard deviation for the GPA of all nontraditional students is fU - 3.35 and (T = .6 . Suppose that a random sample of n = 100 nontraditional students is selected from the population of all nontraditional students, and the GPA of each students is determined. Then .V , the sample mean, will be approximately normally distributed (because of the Central Limit theorem). Calculate f.lx and 7, What do we call the symbol 7x ? Describe the sampling distribution of X , the average GPA of nontraditional student sample. What is the approximate probability that the non-traditional student sample has a mean GPA between 3.20 and 3.50? That Exceeds 3.40?

Solution

a)
Mean ( u ) =3.35
Standard Deviation ( sd )=0.6/ Sqrt ( 100 ) = 0.06
Number ( n ) = 100
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
b)
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 3.2) = (3.2-3.35)/0.6/ Sqrt ( 100 )
= -0.15/0.06
= -2.5
= P ( Z <-2.5) From Standard Normal Table
= 0.00621
P(X < 3.5) = (3.5-3.35)/0.6/ Sqrt ( 100 )
= 0.15/0.06 = 2.5
= P ( Z <2.5) From Standard Normal Table
= 0.99379
P(3.2 < X < 3.5) = 0.99379-0.00621 = 0.9876                  
c)
P(X > 3.4) = (3.4-3.35)/0.6/ Sqrt ( 100 )
= 0.05/0.06= 0.8333
= P ( Z >0.8333) From Standard Normal Table
= 0.2023