Scott and Dan have to complete 2 homeworks tonight: one for the physics class an

Question

Scott and Dan have to complete 2 homeworks tonight: one for the physics class and one for the Spanish class. Scott and Dan work on their homeworks independently. The time (in minutes) Scott and Dan spend on the hw for the physics class are X_1 ~ N(100, 729) and X_2 ~ N(90, 841), respectively. And the time Scott and Dan spend on the hw for the Spanish class are Y_1 ~ N(40, 121) and Y_2 ~ N(48, 169), respectively. a) Find the probability that Scott will not finish his two homeworks within 3 hours. b) Find the probability that Scott will complete his two homeworks earlier than Dan by at least 20 minutes. c) Who has the smaller expected time needed to complete the two homeworks, Scott or Dan? Justify your answer.

Explanation / Answer

a) here mean time for scott to finish two homework =100+40=140

and std deviation =(729+121)1/2 =29.1548

hence P(X>180)=1-P(Z<(180-140)/29.1548)=1-0.9150=0.0850

b) mean time for Dan =90+48 =138

and std deviation =(841+169)1/2 =31.7805

hence mean time of their differnece A=X-Y =140-138 =2

and std deviation =(29.15482+31.78052)1/2 =43.1277

hence P(A<-20) =P(Z<(-20-2)/43.1277) =P(Z<-0.5101)=0.3050

c) from above Dan has smaller expected time; for E(Y)=138 whjile E(X)=140

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