From the standpoint of industrial microbiology, microorganisms can be considered

Question

From the standpoint of industrial microbiology, microorganisms can be considered chemical factories in miniature. They have the capacity to convert a raw material into end products. It is also possible to manipulate microorganism genetically to produce new products. This process is called recombinant DNA technology. A newly designed microbe filter used for engineering of microorganisms to produce valuable chemical substance is subjected to a life test. The lifetime RV X , in weeks, is modeled with a gamma distribution with mean 8 weeks and variance 32 weeks. If the test is terminated after t weeks, what value of t has only 4% of all microbe filters still functional at termination?

Explanation / Answer

Solution:

Gamma distribution mean ?? = 8

and variance=??2 = 64

hence ? = 8

and ? = 1

this is a gamma distribution with relaibilty R(t) =e-t/?

from above 0.04 =e-t/8

taking log on both sides t= -8 log(0.04) = 11.1835

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