Z-test and Confidence Intervals | IB Math AIHL | Perplex

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Inference & Hypotheses (Lesson 5/6)

Z-test and Confidence Intervals

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Discussion

A machine cuts precision parts for use in airplanes. The time, X seconds, taken to cut each part is normally distributed with a standard deviation of 12, but known mean:

X∼N(μ,122)

The quality control engineer samples the time taken to manufacture 8 parts:

45,47,49,51,53,55,57,59

(a)

What's the best guess the engineer can make for the average μ?

Solution:

The machine’s average cutting time is unknown, so the best single guess is the sample average. With the eight times 45, 47, 49, 51, 53, 55, 57, 59, notice they are evenly spaced and symmetric about the midpoint. So the average is the midpoint of the smallest and largest:

xˉ=245+59=52

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