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 5 mm and a standard deviation of 0.03 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 ---Select--- ✓with mean 5- 20x = 5+20x = mm and standard deviation (b) When no unusual circumstances are present, we expect x to be within 20 of 5 mm, the desired value. An x value farther from 5 mm than 20 is interpreted as an indication of a problem that needs attention. Calculate 5 ± 20%. mm mm mm. (c) Referring to part (b), what is the probability that a sample mean will be outside 5 ± 20 just by chance (that is, when there are no unusual circumstances)? (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 5.03 mm. What is the probability that a problem will be detected when the next sample is taken? (Hint: This will occur if x > 5 + 20 orx < 5-20 when μ = 5.03. Round your answer to four decimal places.)
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 5 mm and a standard deviation of 0.03 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 ---Select--- ✓with mean 5- 20x = 5+20x = mm and standard deviation (b) When no unusual circumstances are present, we expect x to be within 20 of 5 mm, the desired value. An x value farther from 5 mm than 20 is interpreted as an indication of a problem that needs attention. Calculate 5 ± 20%. mm mm mm. (c) Referring to part (b), what is the probability that a sample mean will be outside 5 ± 20 just by chance (that is, when there are no unusual circumstances)? (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 5.03 mm. What is the probability that a problem will be detected when the next sample is taken? (Hint: This will occur if x > 5 + 20 orx < 5-20 when μ = 5.03. Round your answer to four decimal places.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
Related questions
Question
answer D ONLY
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill