placed under a known load (force). Smaller beams made of the same material will then be used as springs to protect electronics. The manufacturer needs the beam to flex on average 5.0 mm, with 95 % of all samples having a flex between 4.7 mm and 5.3 mm. After testing the flex of 20 samples, the following numbers are found: 20 i=1 x₁ = 102.2 mm 20 i=1 2 Xi = 523.7 mm² Each sample has the flex measured to the nearest 0.1 mm using electronic calipers. What is the mean flex found using 20 samples? What is the sample standard deviation of flex found using 20 samples?

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3. An experiment is conducted to measure the flex (amount of bending) in a thin composite beam when
placed under a known load (force). Smaller beams made of the same material will then be used as
springs to protect electronics.
The manufacturer needs the beam to flex on average 5.0 mm, with 95 % of all samples having a flex
between 4.7 mm and 5.3 mm.
After testing the flex of 20 samples, the following numbers are found:
(d)
(e)
20
(f)
(g)
i=1
Each sample has the flex measured to the nearest 0.1 mm using electronic calipers.
(a)
What is the mean flex found using 20 samples?
What is the sample standard deviation of flex four using 20 samples?
What is the 95% confidence interval for an individual sample? (Not true mean
this time!) That is, in what range would we expect the flex of 95 % of the samples to be
found?
x₁ = 102.2 mm
20
Σχι" = 523.7 mm2
Xi
i=1
Does the set of samples used satisfy the desired failure rate?
Explain the reasoning behind your answer.
What percent difference is there between the actual average flex and the desired
flex? Treat the desired flex as the "true" value.
Discuss the accuracy and precision of the experiment performed.
Write a conclusion for the experiment performed.
Transcribed Image Text:3. An experiment is conducted to measure the flex (amount of bending) in a thin composite beam when placed under a known load (force). Smaller beams made of the same material will then be used as springs to protect electronics. The manufacturer needs the beam to flex on average 5.0 mm, with 95 % of all samples having a flex between 4.7 mm and 5.3 mm. After testing the flex of 20 samples, the following numbers are found: (d) (e) 20 (f) (g) i=1 Each sample has the flex measured to the nearest 0.1 mm using electronic calipers. (a) What is the mean flex found using 20 samples? What is the sample standard deviation of flex four using 20 samples? What is the 95% confidence interval for an individual sample? (Not true mean this time!) That is, in what range would we expect the flex of 95 % of the samples to be found? x₁ = 102.2 mm 20 Σχι" = 523.7 mm2 Xi i=1 Does the set of samples used satisfy the desired failure rate? Explain the reasoning behind your answer. What percent difference is there between the actual average flex and the desired flex? Treat the desired flex as the "true" value. Discuss the accuracy and precision of the experiment performed. Write a conclusion for the experiment performed.
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