LED bulbs: mean = 2,300 days, standard deviation = 230 days incandescent bulbs: mean = 100 days, standard deviation = 10 days Estimate the proportion of LED bulbs that are expected to burn out before getting within 1 standard deviation of the mean (before 2,070 days). Estimate the proportion of incandescent bulbs that are expected to burn out before getting within 1 standard deviation of the mean (before 90 days). Estimate the proportion of LED bulbs that are expected to burn out after getting more than 1 standard deviation greater than the mean (after 2,530 days). Estimate the proportion of incandescent bulbs that are expected to burn out after getting more than 1 standard deviation greater than the mean (after 110 days).

LED bulbs: mean = 2,300 days, standard deviation = 230 days incandescent bulbs: mean = 100 days, standard deviation = 10 days Estimate the proportion of LED bulbs that are expected to burn out before getting within 1 standard deviation of the mean (before 2,070 days). Estimate the proportion of incandescent bulbs that are expected to burn out before getting within 1 standard deviation of the mean (before 90 days). Estimate the proportion of LED bulbs that are expected to burn out after getting more than 1 standard deviation greater than the mean (after 2,530 days). Estimate the proportion of incandescent bulbs that are expected to burn out after getting more than 1 standard deviation greater than the mean (after 110 days).

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

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The life span of light bulbs is approximately normally distributed. Some statistics about life spans of two different types of light bulbs are listed.
LED bulbs: mean = 2,300 days, standard deviation = 230 days
incandescent bulbs: mean = 100 days, standard deviation = 10 days
Estimate the proportion of LED bulbs that are expected
to burn out before getting within 1 standard deviation of
the mean (before 2,070 days).
Estimate the proportion of incandescent bulbs that are
expected to burn out before getting within 1 standard
deviation of the mean (before 90 days).
Estimate the proportion of LED bulbs that are expected
to burn out after getting more than 1 standard deviation
greater than the mean (after 2,530 days).
Estimate the proportion of incandescent bulbs that are
expected to burn out after getting more than 1 standard
deviation greater than the mean (after 110 days).
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