Upgrading a certain software package requires installation of 68 new files. File

Question

Upgrading a certain software package requires installation of 68 new files. Files are installed consecutively. The installation time is random, but on the average, it takes 15 sec to install one file, with a variance of 11 sec^2. c What is the probability that the whole package is upgraded in less than 12 minutes? A new version of the package is released. It requires only N new files to be installed, and it is promised that 95% of the time upgrading takes less than 10 minutes. Given this information, compute N.

Explanation / Answer

4.31) mean time of 68 files =15*68 =1020

and std deviation of time taken to install 68 files=(11*68)1/2 =27.35

therefore proability that whole package takes less then 12 min(720 sec)=P(X<720)=P(Z<(720-1020)/27.35)

=P(Z<-10.9691)=0.0000

b) for N file mean time =15N

and std deviation =(11N)1/2

hence P(X<600)>0.95

(600-15N)/(11N)1/2 >1.6449

N =37

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