mean of population = 

variance of population = [(2-6)²+(3-6)²+(6-6)²+(8-6)²+(11-6)²]/5 = 10.8

standard deviation of population = √(var) = √(10.8) = 3.286335345


  [2,2]  mean = 2    var =  0
  [2,3]  mean = 2.5  var =  0.25
  [2,6]  mean = 4    var =  4
  [2,8]  mean = 5    var =  9
 [2,11]  mean = 6.5  var = 20.25
  [3,3]  mean = 3    var =  0
  [3,6]  mean = 4.5  var =  2.25
  [3,8]  mean = 5.5  var =  6.25
 [3,11]  mean = 7    var = 16
  [6,6]  mean = 6    var =  0
  [6,8]  mean = 7    var =  1
 [6,11]  mean = 8.5  var =  6.25
  [8,8]  mean = 8    var =  0
 [8,11]  mean = 9.5  var =  2.25
[11,11]  mean = 11   var =  0
------------------------------
 sums           90         67.5

mean of sample means = 90/15 = 6

variance of sample means = 67.5/5 = 13.5

standard deviation of sample means = √13.5 = 3.674234614

(a) the mean of the population, μ=6
(b) the standard deviation of the population, σ=3.286335345
(c) the mean of the sampling distribution of means, μx̄=6
(d) the standard deviation of the sampling distribution of means, i.e., the
standard error of means. σx̄=3.674234614

Edwin