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Refer to Exercise 4.66. Suppose that five bearings are
Chapter 4, Problem 163SE(choose chapter or problem)
Problem 163SE
Refer to Exercise 4.66. Suppose that five bearings are randomly drawn from production. What is the probability that at least one is defective?
Reference
A machining operation produces bearings with diameters that are normally distributed with mean 3.0005 inches and standard deviation .0010 inch. Specifications require the bearing diameters to lie in the interval 3.000 ± .0020 inches. Those outside the interval are considered scrap and must be remachined. With the existing machine setting, what fraction of total production will be scrap?
a Answer the question, using Table 4, Appendix 3.
b Applet Exercise Obtain the answer, using the applet Normal Probabilities.
Questions & Answers
QUESTION:
Problem 163SE
Refer to Exercise 4.66. Suppose that five bearings are randomly drawn from production. What is the probability that at least one is defective?
Reference
A machining operation produces bearings with diameters that are normally distributed with mean 3.0005 inches and standard deviation .0010 inch. Specifications require the bearing diameters to lie in the interval 3.000 ± .0020 inches. Those outside the interval are considered scrap and must be remachined. With the existing machine setting, what fraction of total production will be scrap?
a Answer the question, using Table 4, Appendix 3.
b Applet Exercise Obtain the answer, using the applet Normal Probabilities.
ANSWER:
Solution 163SE
Step1 of 2:
Let us consider a random variable Y it presents the number of bearings produced by a machine.
Here Y follows normal distribution with mean and standard deviation
The bearing diameters to lie in the interval 3.000 ± 0.0020 inches.
We need to find the probability that at least one is defective.
Step2 of 2:
Let,
3.000 ± 0.0020
(2.998, 3.002)
Consider,
The Z statistics is given by: