4.1 The breaking strength, R, of a cable can be assumed to be a normal random va

Question

4.1 The breaking strength, R, of a cable can be assumed to be a normal random variable with a mean value of 80 kip and a standard deviation of 20 kip. (a) If a load, P, of magnitude 60 kip is hung from the cable, calculate the probability of failure of the cable. (b) The magnitude of P cannot be determined with certainty. Suppose it could be either 40 kip or 60 kip, and the corresponding PMFs are shown in the figure below. Calculate the probability of failure of the cable. (c) If the cable breaks, what is the probability that the load was 40 kip? 0.7 Pp(p) 0.3 P(kips) 40 60

Explanation / Answer

a) probability of failure =P(X<60)=P(Z<(60-80)/20)=P(Z<-1)=0.1587

b)probability of failure =P( load of 40 and cable breaks+load of 60 and cable breaks)

=0.3*P(Z<-2)+ 0.7*P(Z<-1) =0.3*0.02275+0.7*0.1587=0.1179

c)probability that load was 40kip given cable breaks =P(load of 40 and cable breaks)/P(cable breaks)

=0.3*0.02275/0.1179 =0.0579

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

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