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Will Byers wants to buy a new computer to spy on Russians with, but needs a...

Will Byers wants to buy a new computer to spy on Russians with, but needs a very good one. There is a computer company that claims that one of their models will get a 3DMark performance test score of 20000 (or greater). He buys a sample of 8 computers and got the following scores: 19883, 19825, 19938, 20008, 19984, 20044, 19807, 19869. Assume that the scores are normally distributed. Will is suspicious that the company’s claim is false. He manages to convince the company to allow him to test a larger sample of 150 computers at their warehouse for free. He found that only 60 of them scored 20000 or higher.

(a) Construct an 96% Confidence Interval Upper Bound for the overall proportion of performance test scores that are at least 20000.

(b) Construct an 96% 2-sided Confidence Interval for the overall proportion of performance test scores that are at least 20000.

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