Question

A. 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	56
Woon Junge	50
Ernie DeBrul	52
Jan Niles	49
Molly Camp	49
Rachel Myak	53

How many samples of size 2 are possible?

     

No of samples

    

.	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)56,4956,5056,5249,5350,49
(Click to select)56,5256,5050,4956,4949,53
(Click to select)56,4956,5250,4949,5356,50
(Click to select)49,5356,5250,4956,5056,49
(Click to select)56,5349,5349,4956,4956,50
(Click to select)56,4950,5249,5349,4956,50
(Click to select)49,5350,4956,4949,4956,50
(Click to select)50,4949,5356,5049,4956,49
(Click to select)56,5056,4949,5350,5349,49
(Click to select)52,4949,4956,4949,5356,50
(Click to select)49,4949,5356,5056,4952,49
(Click to select)56,4949,5350,4952,5356,50
(Click to select)56,5049,5356,4949,4956,52
(Click to select)56,5056,4950,5349,5356,52
(Click to select)56,5056,5252,5356,4949,53

      

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

              

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

B.

Power+, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 38 hours and a standard deviation of 5.9 hours. As a part of its quality assurance program, Power+, Inc. tests samples of 16 batteries.

    

	What can you say about the shape of the distribution of the sample mean?
	Normal Uniform Binomial

         

)	What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

          

Standard error

       

What proportion of the samples will have a mean useful life of more than 39 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

          

Probability

)	What proportion of the sample will have a mean useful life greater than 36.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

         

Probability

What proportion of the sample will have a mean useful life between 36.5 and 39 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

         

Probability

C.

Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,856 pounds and the standard deviation is 105 pounds. Assume that the population follows the normal distribution. Forty six trucks are randomly selected and weighed. Within what limits will 95% of the sample means occur? (Round your answers to the nearest whole number.)

   

The limits are

and

Answer 1

Total number of sales representatives = 6

Number of samples of size 2 are possible = ⁶C₂ = 6!/2!(6-2)! = 15

S.N	SOLD	SUM	MEAN
1	(56,50)	106	53
2	(56,52)	108	54
3	(56,49)	105	52.5
4	(56,49)	105	52.5
5	(56,53)	109	54.5
6	(50,52)	102	51
7	(50,49)	99	49.5
8	(50,49)	99	49.5
9	(50,53)	103	51.5
10	(52,49)	101	50.5
11	(52,49)	101	50.5
12	(52,53)	105	52.5
13	(49,49)	98	49
14	(49,53)	102	51
15	(49,53)	102	51

Mean of sample mean = 1/15 (53+54+52.5+52.5+54.5+51+49.5+49.5+51.5+50.5+50.5+52.5+49+51+51) = 51.5

Population mean = 1/6 (56+50+52+49+49+53) = 51.5

the shape of the distribution of the sample mean is Normal

B)

the shape of the distribution of the sample mean is Normal

Standard error of the distribution of the sample mean = standard deviation/√n = 5.9/√16 = 1.475

P( x̅> 39) = P((x̅-μ)/σ/√n) > (39-38)/1.475) = P(z > 0.68) = 0.2482

P( x̅> 36.5) = P((x̅-μ)/σ/√n) > (36.5-38)/1.475) = P(z > -1.02) = 0.8461

P(36.5 < x̅ < 39) = P((36.5 - 38)/1.475 < Z < (39 - 38)/1.475) = P(Z < 0.68) - P(Z < -1.02) = 0.5978

C)

z for 95% CI=1.96

upper limit=mean+1.96(standard deviation/√46) = 6,856+1.96(105/ √46) = 6886

lower limit=mean-1.96(standard deviation/√46) = 6,856-1.96(105/√46) = 6826

The limits are 6826 and 6886