Shafts manufactured for use in optical storage devices have diameters that are normally distributed with mean μ = 0.652 cm and standard deviation σ = 0.003 cm. The specification for the shaft diameter is 0.650 ± 0.005 cm.a) Find the 85th percentile of the shaft diameter.b) If 10 shafts are randomly selected, what is the probability that at most 1 shaft does not meet the specification?

a) To find the 85th percentile of the shaft diameter, we need to use the properties of the normal…

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 14PPS

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Shafts manufactured for use in optical storage devices have diameters that are normally distributed with mean μ = 0.652 cm and standard deviation σ = 0.003 cm. The specification for the shaft diameter is 0.650 ± 0.005 cm.

a) Find the 85th percentile of the shaft diameter.

b) If 10 shafts are randomly selected, what is the probability that at most 1 shaft does not meet the specification?

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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