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

expected trime for Scott(X) to finish two home work =100+90=190

and std deviation=(729+841)1/2 =39.62

expected trime for Dan(Y) to finish two home work =40+48=88

and std deviation=(121+169)1/2 =17.03

a) hence P(X>180)=1-P(Z<(180-190)/39.62) =1-P(Z<-0.2524)=1-0.4004=0.5996

b)for mean of X-Y =102

and std deviation =(39.622+17.032)1/2 =43.13

P(X-Y<-20)=P(Z<(-20-102)/43.1277)=P(Z<-2.8288)=0.0023

c) from above as expected time diffierence of scott and Dan is 102 minutes, hence expected time is smaller for Dan,

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.