Alaboratory scale is known to have a standard deviation of σ = 0.001 gram in repeated weighings. Scale readings in repeated weighings are Normally distributed, with mean equal to the true weight of the specimen. Three weighings of a specimen on this scale give 1.4131, 1.4167, and 1.4101 grams. A 95% confidence interval for the true weight of this specimen is

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Zechariah Curtis

1 April, 06:44

Alaboratory scale is known to have a standard deviation of σ = 0.001 gram in repeated weighings. Scale readings in repeated weighings are Normally distributed, with mean equal to the true weight of the specimen. Three weighings of a specimen on this scale give 1.4131, 1.4167, and 1.4101 grams. A 95% confidence interval for the true weight of this specimen is

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Darwin Zuniga · Answer 1

The 95% confidence interval for the true weight is 1.4103 and 1.41587 grams.

Explanation:

If we sorted by ascending order the three weighings given and we asumme these 3 weighings as extreme values and mean, we can calculate the 95% confidence interval. Using the formula for Normal distributions we know that 95% intervals are 1,96 times standard deviation from the the mean, then Mean (1.4131) ± 1.96*Standard deviation (0.001) = 1.4103 and 1.41587