-40 points Devore S 4 E.65 suppose that X has a qan ma ds rit tion with mean val

Question

-40 points Devore S 4 E.65 suppose that X has a qan ma ds rit tion with mean value 37.5 ms and standard da at n 21 G suqgasted by te at cle Con tation Let X darote th data tra ster tme nns in a qnd computio system the time regu red or data trans er betaean a wo kar computar and a master co Time of Grid Computing with Cata Transfer Times that Folow Grmma Distrbution,' ter (a) what are the values of aand Round your answers to four decimal placs.) (b) what is the probabilty that data transfer time exceeds 49 ms? Round your ansier to three decimal places.) [c] what l: the probabilty that data transfer tine ls between 4 and 72 mg? Round Ynur answer tn three dedmal placas.] You mar need to use the apppriste table in the Appendix of Tables to ansve this question, Noed Help? Hrd Show My Work eurkow

Explanation / Answer

a)

E(X) = a/b = 37.5

Var(X) = a/b^2 = 21.6^2

solving we get

a = 3.014081

b = 0.08037

b)

P(X> 49)

=1-pgamma ( 49,3.014081,0.08037)
[1] 0.2498836

c)

pgamma ( 72,3.014081,0.08037) - pgamma ( 49,3.014081,0.08037)
[1] 0.1766417

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