Answered: The length of pins produced by a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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The length of pins produced by a manufacturing plant is known to have population
mean µ = 215 mm and population SD σ = 19 mm. One of the clients of that manufacturing
plant specifies a pin to be a non-defective if its length (in mm) lies in the interval (197, 239);
a pin is considered as defective by this client if this specification is not met. Pins come out
through an automated process in boxes, with each box containing 32 pins. A box containing
more than 3 defective pins is treated by this client as a box of ‘unacceptable quality’. What
is the probability that a randomly selected box will be of unacceptable quality? State your
assumptions, if any, explicitly.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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