Answered: A company manufactures light bulbs. The…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A company manufactures light bulbs. The company wants the bulbs to have a mean life span of

994

hours. This average is maintained by periodically testing random samples of

light bulbs. If the t-value falls between

−t0.99

and

t0.99,

then the company will be satisfied that it is manufacturing acceptable light bulbs. For a random sample, the mean life span of the sample is

1002

hours and the standard deviation is

hours. Assume that life spans are approximately normally distributed. Is the company making acceptable light bulbs? Explain.

A company manufactures light bulbs. The company wants the bulbs to have a mean life span of 994 hours. This
average is maintained by periodically testing random samples of 25 light bulbs. If the t-value falls between - to.99 and
to.99, then the company will be satisfied that it is manufacturing acceptable light bulbs. For a random sample, the
mean life span of the sample is 1002 hours and the standard deviation is 22 hours. Assume that life spans are
approximately normally distributed. Is the company making acceptable light bulbs? Explain.
The company
making acceptable light bulbs because the t-value for the sample is t =
(Round to two decimal places as needed.)
and to.99
-0.
=

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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