Question 5.22: The lengths of bolts manufactured by a certain process are k......

ISE Principles of Statistics for Engineers and Scientists [987713]

The lengths of bolts manufactured by a certain process are known to be normally distributed. In a sample of 30 bolts, the average length was 10.25 cm, with a standard deviation of 0.20 cm. Find a tolerance interval that includes 90% of the lengths of the bolts with 95% confidence.

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We have $\overline{X} = 10.25$ and s = 0.20. The value of 𝛾 is 0.10 and the value of 𝛼 is 0.05. The sample size is n = 30. From Table A.4, we find that $k_{n, \alpha, \gamma} = 2.1398$ . The tolerance interval is therefore 10.25 ± 2.1398(0.20), or (9.82, 10.68).

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