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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

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.

The Video Game Satisfaction Survey Instrument
Strongly Strongly
Statement Disagree 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

Here, the level of agreement for each statement is measured on a 7-point Likert scale. Purchaser satisfaction will be measured by adding the purchasers 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. 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
37 37 17 33 43
40 43 30 43 25
27 38 45 42 32
33 20 46 24 45
34 18 37 16 25
24 35 22 26
15 22 21 45
42 36 31 40
31 25 19 28
17 39 45 44
35 40 18 35
25 36 22 35
26 46 41 40
16 27 29 23
35 27 36 24

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 scoresanswer to 3 decimal places.)

Most of the scores would fall between____and_____

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

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