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Chapter 4: Q143E (page 277)

Lead in metal shredder residue. On the basis of data collectedfrom metal shredders across the nation, the amount xof extractable lead in metal shredder residue has an approximateexponential distribution with meanθ= 2.5 milligramsper liter (Florida Shredder’s Association).

a. Find the probability that xis greater than 2 milligramsper liter.

b. Find the probability that xis less than 5 milligrams perliter.

Short Answer

Expert verified

a.Px>2=.0068

b.Px<5=0.9999

Step by step solution

01

Given information

X is an exponential random variable andθ=2.5 .

02

Define the probability density function

The p.d.f of X is

fx=θe-θx;x≥0=2.5e-2.5x

03

Calculate P(x>2)

a

Px>2=1-Px≤2=1-∫022.5-2.5xdx=1-2.5∫02e-2.5xdx=1-525-2e-552=1-e-5e-5-1=1-0.9932=0.0068

Hence, the probability of x that x is greater than 2 milligrams per liter is 0.0068.

04

Calculate P(x<5)

b

Px<5=∫052.5e-2.5xdx=2.5∫05e-2.5xdx=525-2e-25252=e-252e-252-1=0.9999

Hence, the probability of x that x is less than 5 milligrams per liter is 0.9999.

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Most popular questions from this chapter

On-site treatment of hazardous waste. The Resource Conservation and Recovery Act mandates the tracking and disposal of hazardous waste produced at U.S. facilities. Professional Geographer (February 2000) reported the hazardous-waste generation and disposal characteristics of 209 facilities. Only 8 of these facilities treated hazardous waste on-site. Use the hypergeometric distribution to answer the following:

a. In a random sample of 10 of the 209 facilities, what is the expected number in the sample that treat hazardous waste on-site? Interpret this result.

b. Find the probability that 4 of the 10 selected facilities treat hazardous waste on-site.

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Suppose x is a normally distributed random variable with μ= 11 and σ= 2. Find each of the following:

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