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?

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:

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