Question

Exercise 8-30

The Appliance Center has six sales representatives at its North Jacksonville outlet. Listed below is the number of refrigerators sold by each last month.

   

Sales Representative	Number Sold
Zina Craft	54
Woon Junge	51
Ernie DeBrul	52
Jan Niles	47
Molly Camp	50
Rachel Myak	51

a.	How many samples of size 2 are possible?

     

No of samples

    

b.	Select all possible samples of size 2 and compute the mean number sold. (Round Mean values to 1 decimal place.)

     

Sold	Mean
(Click to select)54,5254,4754,5150,4747,51
(Click to select)54,4750,4754,5247,5154,51
(Click to select)47,5154,4754,5154,5250,47
(Click to select)47,5154,5154,5250,4754,50
(Click to select)54,4747,5152,5150,5154,51
(Click to select)47,5150,5151,5254,4754,51
(Click to select)54,4747,5150,5154,5151,47
(Click to select)52,5154,4751,5054,5147,51
(Click to select)54,5151,5147,5152,5154,47
(Click to select)47,5152,5154,4752,4754,51
(Click to select)47,5152,5052,5154,5154,47
(Click to select)50,4754,5152,5147,5154,47
(Click to select)47,5054,5254,4747,5154,51
(Click to select)47,5154,5254,5154,4751,51
(Click to select)54,5154,5254,4747,5150,51

      

d.	What is the mean of the population? What is the mean of the sample means? (Round your answers to 2 decimal places.)

           

Mean of sample mean
Population mean

              

f.	What is the shape of the distribution of the sample mean?
	Uniform Normal

Answer 1

Answer :

given data :-

we have a tabular form with data

Sales Representative	Number Sold
Zina Craft	54
Woon Junge	51
Ernie DeBrul	52
Jan Niles	47
Molly Camp	50
Rachel Myak	51

(a). now we need to find out the  How many samples of size 2 are possible ?

n = 6

r = 2

now we using the combination formula

= n! / r!(n-r)!

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

= 720 /2(24)

= 720 / 48

= 15

(b).possible samples of size 2 and compute the mean number sold :

54,51	(54+51)/2 = 52.5
54,52	(54+52)/2 = 53
54,47	(54+47)/2 = 49
54,50	(54+50)/2 = 52
54,51	(54+51)/2 = 52.5
51,52	(51+52)/2 = 51.5
51,47	(51+47)/2 = 49
51,50	(51+50)/2 = 50.5
51,51	(51+51)/2 = 51
52,47	(52+47)/2 = 49.5
52,50	(52+50)/2 = 51
52,51	(52+51)/2 = 51.5
47,50	(47+50)/2 =48.5
47,51	(47+51)/2 = 49
50,51	(50+51)/2 = 50.5

(d). the mean of the population and the mean of the sample means :

Mean of sample mean is = (52.5+53+49+52+52.5+51.5+49+50.5+51+49.5+51+51.5+48.5+49+50.5)/15

= 761/15

= 50.73

  Population mean is = (54+51+52+47+50+51)/5

= 305/6

= 50.83

(f).  the shape of the distribution of the sample mean is :

= Normal