Question

A company that produces and markets video game systems wishes to assess its customers' level of satisfaction with a relatively new model, the XYZ-Box. In the six months since the introduction of the model, the company has received 73,219 warranty registrations from purchasers. The company will select a random sample of 65 of these registrations and will conduct telephone interviews with the purchasers. Specifically, each purchaser will be asked to state his or her level of agreement with each of the seven statements listed on the survey instrument given in the following table.. Here, the level of agreement for each statement is measured on a 7-point Likert scale Purchaser satisfaction will be measured by adding the purchaser's responses to the seven statements. It follows that for each consumer the minimum composite score possible is 7 and the maximum is 49. Furthermore, experience has shown that a purchaser of a video game system is "very satisfied" if his or her composite score is at least 42.

The Video Game Satisfaction Survey Instrument

Statement	Strongly Disagree						Strongly Agree
The game console of the XYZ-Box is well designed.	1	2	3	4	5	6	7
The game controller of the XYZ-Box is easy to handle.	1	2	3	4	5	6	7
The XYZ-Box has high quality graphics capabilities.	1	2	3	4	5	6	7
The XYZ-Box has high quality audio capabilities.	1	2	3	4	5	6	7
The XYZ-Box serves as a complete entertainment center.	1	2	3	4	5	6	7
There is a large selection of XYZ-Box games to choose from.	1	2	3	4	5	6	7
I am totally satisfied with my XYZ-Box game system.	1	2	3	4	5	6	7

Suppose that when the 65 customers are interviewed, their composite scores are as given in the following table.

Composite Scores for the Video Game Satisfaction Rating Case
38	45	43	40	39
46	48	45	43	44
38	39	47	43	41
44	41	41	46	45
38	38	49	43	39
48	46	48	39
45	40	44	38
46	40	43	38
43	41	44	41
38	40	45	38
43	40	42	38
46	47	39	38
48	42	44	46
46	45	47	43
45	40	38	46

Using the data, estimate limits between which most of the 73,219 composite scores would fall. Also, estimate the proportion of the 73,219 composite scores that would be at least 42. (Round your proportion of scores answer to 2 decimal places.)

Most of the scores would fall between _______ and _______  

An estimate of the proportion of scores that would be at least 42 = _______ %

Answer 1

Answer:

	score
n	65
mean	42.63
sample standard deviation s	3.33

Most of the scored falls between 3 standard deviation limits.

Mean – 3s	32.63
mean + 3s	52.63

Most of the scored would fall between 32.63 and 52.63

since 73219 is very large, we use z distribution to find proportion.

Z value for 42 is z =(42-42.63)/3.33 = -0.19

P( x ≥42) = P( z > -0.19) =0.5753

An estimate of proportion of scores that would be atleast 42 = 57.53%

Answer 2

so to do this question, the answer to the "most" part is just the lowest number and highest number. And then second part is literally counting the numbers less than 42 and dividing it by 65 than 1 minus that decimal.

 eg: 35 numbers are less than 42 therefore 35/65=x and then 1-x *100 is the answer