Question 5.22: The lengths of bolts manufactured by a certain process are k...
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 em, with a standard deviation of 0.20 em. Find a tolerance interval that includes 90% of the lengths of the bolts with 95% confidence.
We have \bar{X}=10.25 and s = 0.20. The value of ϒ 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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