Five bundles of pencils contain the quantities shown a How m

          Five bundles of pencils contain the quantities shown

a. How many different samples of 2 bundles ea are there?

b. List all possible samples of size 2 and compute the mean of each sample

c. calculate the population mean and compare it to the mean of the sampling

Bundle

Number

of pencils

1

10

2

6

3

10

4

11

5

12

Solution

A) Samples 1,3 are alike, 2,4,5 are differnt

Thus there are 4 different samples with 10 repeated 2 times

b) Sample space=

2 taken from 2 identical and 3 more different

= 2c0(3C2) + 2C1(3C1) +2c2(3c0)

=3+6+1=10

b) Sample space would consist of 10 as

(1,3) (1,2) (1,4)(1,5) (2,1) (2,4) (2,5) (3,4)(3,5)(4,5)

Mean = [2,1.5, 2.5, 3,1.5,3,3.5,3.5,4,4.5]

c) Population mean = average of all means = 29/10 =2.9