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(d) Suppose that a machine used to apply the coating is out of adjustment, resulting in a mean coating thickness of 3.05 mm. What is the probability that a problem will be detected when the next sample is taken? (Hint: This will occur if x > 3+20orx <3 -20% when = 3.05. Round your answer to four decimal places.)

(d) Suppose that a machine used to apply the coating is out of adjustment, resulting in a mean coating thickness of 3.05 mm. What is the probability that a problem will be detected when the next sample is taken? (Hint: This will occur if x > 3+20orx <3 -20% when = 3.05. Round your answer to four decimal places.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 3 mm and a standard deviation of 0.05 mm. Suppose that the process will be monitored by selecting a random sample of 16 drives from each shift's production and determining x, the mean coating thickness for the sample. USE SALT (a) Describe the sampling distribution of x for a random sample of size 16. The distribution of X is normal ✓with mean 3 mm mm and standard deviation 0.0125 x (b) When no unusual circumstances are present, we expect x to be within 20 of 3 mm, the desired value. An x value farther from 3 mm than 20 is interpreted as an indication of a problem that needs attention. Calculate 3 ± 20% 3- 20 = 2.975 3 + 20 = 3.025 mm mm. (c) Referring to part (b), what is the probability that a sample mean will be outside 3 ± 20 just by chance (that is, when there are no unusual circumstances)? (Round your answer to four decimal places.) 0.0455 (d) Suppose that a machine used to apply the coating is out of adjustment, resulting in a mean coating thickness of 3.05 mm. What is the probability that a problem will be detected when the next sample is taken? (Hint: This will occur if > > 3 + 20 or < 3-20 when μ = 3.05. Round your answer to four decimal places.)
Transcribed Image Text:The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 3 mm and a standard deviation of 0.05 mm. Suppose that the process will be monitored by selecting a random sample of 16 drives from each shift's production and determining x, the mean coating thickness for the sample. USE SALT (a) Describe the sampling distribution of x for a random sample of size 16. The distribution of X is normal ✓with mean 3 mm mm and standard deviation 0.0125 x (b) When no unusual circumstances are present, we expect x to be within 20 of 3 mm, the desired value. An x value farther from 3 mm than 20 is interpreted as an indication of a problem that needs attention. Calculate 3 ± 20% 3- 20 = 2.975 3 + 20 = 3.025 mm mm. (c) Referring to part (b), what is the probability that a sample mean will be outside 3 ± 20 just by chance (that is, when there are no unusual circumstances)? (Round your answer to four decimal places.) 0.0455 (d) Suppose that a machine used to apply the coating is out of adjustment, resulting in a mean coating thickness of 3.05 mm. What is the probability that a problem will be detected when the next sample is taken? (Hint: This will occur if > > 3 + 20 or < 3-20 when μ = 3.05. Round your answer to four decimal places.)
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