Answered: One step in the manufacture of a…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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One step in the manufacture of a certain metal clamp involves the drilling of four holes. In a sample of 100 clamps, the average time needed to complete this step was 80 seconds and the standard deviation was 15 seconds.

a. Find a 95% confidence interval for the mean time needed to complete the step.

b.Find a 99.5% confidence interval for the mean time needed to complete the step.

c.What is the confidence level of the interval (78,82)?

d.How many clamps must be sampled so that

a 95% confidence interval specifies

the mean to within ±1 seconds?

e.How many clamps must be sampled so that a 99.5% confidence interval specifies the mean to within ±1 seconds?

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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