Please Help! (Sampling Distributions)


New Member
I'm struggling with these two problems, i'll really appreciate any help, thanks in advance = )
1) Obtain the probablility, by counting, of each possible sample if a random sample of size 2 is taken from
a. a finite population of size 3
b. a finite population of size 4

2) The mean of a random sample of size n=100 is going to be used to estimate the mean daily milk production of a very large herd of dairy cows. Given that the standard deviation of the population to be sampled is 3.6 quarts, what can we assert about the probabilities that the error of this estimate will be
a. more than .72 quart;
b. less than . 45 quart?
(I got .4452 for part A and .6826 for part B, but i'm not sure if it is correct)
1.a) There are 3C2 possible ways to draw 2 object from a population of size 3 without replacement. Where nCr is "n choose r".

3C2 = 3!/2!(3-2)! = 6/2 = 3

So there are three ways to draw a sample of size 2 from a population of size 3. The probabiliy for each sample is then 1/3.

2. We can model this with the standard normal distribution:
We want to find:

P((Xbar - mu) / (3.6 / sqrt(100)) > 0.72 / (3.6 / sqrt(100)))
= P(Z > 0.72 / (3.6 / 10))
= P(Z > 2) = 0.0228