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31.03.2020 •
Mathematics
Based on data collected from metal shredders across the nation, the amount L of extractable lead in metal shredder residue has an approximate exponential distribution with mean μ = 2.0 milligrams per liter. What is the probability that L is greater than 1.20 milligrams per liter?
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Ответ:
The cumulative distirbution function is given by:
And using the complement rule we have:
Step-by-step explanation:
Previous concepts
The cumulative distribution function (CDF) F(x),"describes the probability that a random variableX with a given probability distribution will be found at a value less than or equal to x".
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
Solution to the problem
For this case we define the random variable L="the amount L of extractable lead in metal shredder residue" and the distirbution for X is given by:
For this case we want this probability:
The cumulative distirbution function is given by:
And using the complement rule we have:
Ответ:
pic of graph?
Step-by-step explanation: