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Chapter 4: Q73E (page 247)

Contaminated gun cartridges. Refer to the investigation of contaminated gun cartridges at a weapons manufacturer, presented in Exercise 4.29 (p. 226). In a sample of 158 cartridges from a certain lot, 36 were found to be contaminated, and 122 were “clean.” If you randomly select 5 of these 158 cartridges, what is the probability that all 5 will be “clean”?

Short Answer

Expert verified

The probability that all 5 will be clean is 0.20.

Step by step solution

01

Given Information

A lot contains 158 cartridges.

N=158M=36N-M=122n=5

02

Hypergeometric Distribution is used to find the probability

The probability is calculated as

px=0=M0×N-MN-0Nn=360×1225-01580=1×207288004769754986=0.26

Therefore, the probability is 0.26.

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Most popular questions from this chapter

Assume that xhas an exponential distribution withθ=3.

Find

a.P(x≤1)

b.P(x>1)

c.P(x=1)

d.P(x≤6)

e.P(2≤x≤10)

4.131 Chemical composition of gold artifacts. The Journal of Open Archaeology Data(Vol. 1, 2012) provided data onthe chemical composition of more than 200 pre-Columbiangold and gold-alloy artifacts recovered in the archaeologicalregion inhabited by the Muisca of Colombia (a.d.600–1800). One of many variables measured was the percentageof copper present in the gold artifacts. Summary statisticsfor this variable follow: mean = 29.94%, median = 19.75%,standard deviation = 28.37%. Demonstrate why the probabilitydistribution for the percentage of copper in thesegold artifacts cannot be normally distributed.

Soft-drink dispenser. The manager of a local soft-drink bottling company believes that when a new beverage dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount at random anywhere between 6.5and 7.5 ounces inclusive. Suppose has a uniform probability

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a.Is the amount dispensed by the beverage machine a discreteor a continuous random variable? Explain.

b. Graph the frequency function forX , the amount of beverage the manager believes is dispensed by the new machine when it is set to dispense 7 ounces.

c. Find the mean and standard deviation for the distribution graphed in part b, and locate the mean and theinterval μ±2σon the graph.

d. Find P(x≥7).

e. FindP(x<6) .

f. FindP(6.5≤x≤7.25) .

g. What is the probability that each of the next six bottles filled by the new machine will contain more than7.25 ounces of beverage? Assume that the amount of beverage dispensed in one bottle is independent of the amount dispensed in another bottle.

4.126 Wear-out of used display panels.Wear-out failure time ofelectronic components is often assumed to have a normaldistribution. Can the normal distribution be applied to thewear-out of used manufactured products, such as coloreddisplay panels? A lot of 50 used display panels was purchasedby an outlet store. Each panel displays 12 to 18 colorcharacters. Prior to the acquisition, the panels had been usedfor about one-third of their expected lifetimes. The data inthe accompanying table (saved in the file) give the failuretimes (in years) of the 50 used panels. Use the techniquesof this section to determine whether the used panel wear-outtimes are approximately normally distributed.

0.01 1.21 1.71 2.30 2.96 0.19 1.22 1.75 2.30 2.98 0.51

1.24 1.77 2.41 3.19 0.57 1.48 1.79 2.44 3.25 0.70 1.54

1.88 2.57 3.31 0.73 1.59 1.90 2.61 1.19 0.75 1.61 1.93

2.62 3.50 0.75 1.61 2.01 2.72 3.50 1.11 1.62 2.16 2.76

3.50 1.16 1.62 2.18 2.84 3.50

How many questionnaires to mail? The probability that a consumer responds to a marketing department’s mailed questionnaire is 0.4. How many questionnaires should be mailed if you want to be reasonably certain that at least 100 will be returned?
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