Answered: The lifetime of lightbulbs are normally…

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

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 )

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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