Question: Ho, Lewer, Peterson, and Riegel worked with the lack of flatness in a particular kind of manufactured steel disk. Fifty different parts of this type were measured for what the students called "wobble," with the results that the 50 (positive) values obtained had mean \(\bar{x}=.0287 \mathrm{in}\). and standard deviation \(s=.0119 \mathrm{in}\).

1. Give a \(95 \%\) two-sided confidence interval for the mean wobble of all such disks.
2. Give a lower bound for the mean wobble possessing a \(95 \%\) confidence level.
3. Suppose that these disks are ordered with the requirement that the mean wobble not exceed .025 in. Assess the strength of the evidence in the students' data to the effect that the requirement is being violated. Show the whole five-step format.
4. Is the requirement of part (c) the same as an upper specification of .025 in. on individual wobbles? Explain. Is it possible for a lot with many individual wobbles exceeding . 025 in. to meet the requirement of part (c) ?
5. Of the measured wobbles, 19 were .030 in. or more. Use this fact and make an approximate \(90 \%\) two-sided confidence interval for the fraction of all such disks with wobbles of at least .030 in.

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