1. (20 pts.) Let Xi, X2, and Xs represent the times (in minutes) necessary to pe
ID: 3340438 • Letter: 1
Question
1. (20 pts.) Let Xi, X2, and Xs represent the times (in minutes) necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values 1, , and 3 and variances of, , and 3. respectively. (a) (10 pts.) If ,-15, 2-25, 3-30 minutes and 1-2, 2m3, 4 minutes, find the mean and the standard deviation of S Xi+X3+Xs the length of time it takes to complete all three repairs. 4555 (b) (5 pts.) Continuing, calculate P(xi +X2+X s 78) (c) (5 pts.) Suppose you are one of 10 customers visiting this service facility that require all three of the repairs to be performed, what is the probability that the average length of time spent at the facility will be more than 65 minutes for the 10 customers.Explanation / Answer
a) here mean time of S =15+25+30=70
and std deviation of S =(22+32+42)1/2 =5.385
b) from normal distribution z score =(X-mean)/std deviation
hence P(S<78)=P(Z<(78-70)/5385)=P(Z<1.4856)=0.9313
c)
for n=10 repairs ;
average time Sbar =70
and std error of mean =std deviation/(n)1/2 =5.385/(10)1/2 =1.7029
therfore probability that average time is more then 65 minutes =P(X>65)=1-P(X<65)=1-P(Z<(65-70)/1.7029)
=1-P(Z<-2.9361)=1-0.0017 =0.9983
please revert for any clarification required.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.