Answered: The lifetime of lightbulbs are normally…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.5: Exponential And Logarithmic Models

Problem 4ECP

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Question

The lifetime of lightbulbs are normally distributed with Mean = 5,059 hours and SD = 277 hours, If we want to be sure that 98% of all bulbs last longer than the advertised figure, what figure should be advertised?

(Tips This is to ask you to find a particular x-value so that P(X > x-value) = 0.9800 or very close;

This can be converted as: P(Z > (x-value - µ)/σ) ) = 0.9800

Now go to the normal table and look inside to find a value that is closest to 0.9800 and find the z-value: you should be able to find z-value = 2.05.

Now, you have (x-value - µ)/σ = 2.05. And you know µ and σ, X-value = µ - z-value *σ )

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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