Question

1. The strengths of individual bars made by a certain manufacturing process are approximately normally distributed with mean 28.4 (in appropriate units). (a) The bars will be unusable if the strength is less than 23.5. To ensure safety, the probability of this must be less than 0.01. i. What value of the standard deviation will just meet the specification if the mean stays the same? ii. Find the range which defines the middle 50% of the bar strength? (b) A customer requires at least 95% of the bars to be stronger than 25.5. Assuming the standard deviation in (a), would the product meet the specification? (c) The bar is considered defective if its strength is less than 23.5. A sample of 10 bars are selected from the manufacturing plant. i. What is the probability of finding exactly one defect in the sample? ii. What is the probability of finding at least one defect in the sample? (d) The manufacturer now claimed that by an improved manufacturing technique the strengths of the bars produced have been increased. To test this claim, a sample of 50 bars is tested and it is found that the mean bar strength is 29.0 with standard deviation of 1.95. Can we support the claim at 0.01 significance level?

          1. The strengths of individual bars made by a certain manufacturing process are approximately normally distributed with mean 28.4 (in appropriate units).
(a) The bars will be unusable if the strength is less than 23.5. To ensure safety, the probability of this must be less than 0.01.
i. What value of the standard deviation will just meet the specification if the mean stays the same?
ii. Find the range which defines the middle 50% of the bar strength?
(b) A customer requires at least 95% of the bars to be stronger than 25.5. Assuming the standard deviation in (a), would the product meet the specification?
(c) The bar is considered defective if its strength is less than 23.5. A sample of 10 bars are selected from the manufacturing plant.
i. What is the probability of finding exactly one defect in the sample?
ii. What is the probability of finding at least one defect in the sample?
(d) The manufacturer now claimed that by an improved manufacturing technique the strengths of the bars produced have been increased. To test this claim, a sample of 50 bars is tested and it is found that the mean bar strength is 29.0 with standard deviation of 1.95. Can we support the claim at 0.01 significance level?

1. The strengths of individual bars made by a certain manufacturing process are approximately normally distributed with mean 28.4 (in appropriate units).
(a) The bars will be unusable if the strength is less than 23.5. To ensure safety, the probability of this must be less than 0.01.
i. What value of the standard deviation will just meet the specification if the mean stays the same?
ii. Find the range which defines the middle 50% of the bar strength?
(b) A customer requires at least 95% of the bars to be stronger than 25.5. Assuming the standard deviation in (a), would the product meet the specification?
(c) The bar is considered defective if its strength is less than 23.5. A sample of 10 bars are selected from the manufacturing plant.
i. What is the probability of finding exactly one defect in the sample?
ii. What is the probability of finding at least one defect in the sample?
(d) The manufacturer now claimed that by an improved manufacturing technique the strengths of the bars produced have been increased. To test this claim, a sample of 50 bars is tested and it is found that the mean bar strength is 29.0 with standard deviation of 1.95. Can we support the claim at 0.01 significance level?

Added by George L.

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