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Statistics / Applied Statistics and Probability for Engineers 6 / Chapter 4.12 / Problem 212SE

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

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Solved: The diameter of the dot produced by a printer is

Chapter 4, Problem 212SE

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QUESTION:

Problem 212SE

The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inch.

(a) Suppose that the specifications require the dot diameter to be between 0.0014 and 0.0026 inch. If the probability that a dot meets specifications is to be 0.9973, what standard deviation is needed?

(b) Assume that the standard deviation of the size of a dot is 0.0004 inch. If the probability that a dot meets specifications is to be 0.9973, what specifications are needed? Assume that the specifications are to be chosen symmetrically around the mean of 0.002.

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QUESTION:

Problem 212SE

The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inch.

(a) Suppose that the specifications require the dot diameter to be between 0.0014 and 0.0026 inch. If the probability that a dot meets specifications is to be 0.9973, what standard deviation is needed?

(b) Assume that the standard deviation of the size of a dot is 0.0004 inch. If the probability that a dot meets specifications is to be 0.9973, what specifications are needed? Assume that the specifications are to be chosen symmetrically around the mean of 0.002.

ANSWER:

Solution:

Step 1 of 3:

Let x follows a Normal distribution with density

f(x) = $\frac{1}{\sigma{}\sqrt{2\Pi{}}}{e}^{-\ \frac{(x\ -\ \mu{}{)}^{2}}{2{\sigma{}}^{2}}}$

Where, $\mu{}$ = 0.002

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