Question

3. The life of a circuit board installed in a newly d nential distribution. The manufacturers hast average life of 17,000 hours installed in a newly designed smart phone follows an expo- e manufacturers has told us that these circuit boards have an (a) Find the probability Find the probability that the life of the circuit board will exceed 4,000 hours. P(x) = n! T*(1-x)" x!(n-x)! (b) Assuming there are 5 such circuit boards installed in series within the smart phone, each one functioning independently of the others, what is the probability that the phone will have a life over 4,000 hours? (c) Our specification requires an 80% survival rate for our phone after 4,000 hours. We contact the manufacturer of the circuit boards that we can use to meet this specification. The lifetimes for these new circuit boards will still follow an expo- nential distribution. We still need to use 5 circuit boards in series in our phone. What average lifetime will these circuit boards have?

Answer 1

Saluhm:- = per hour 17,000 *n Ex ponontial {3) (a) Plx> 4.000) 4000 0.7903 (b) Plall ove 4,000) 10.7903) (x)9 0.30 8 3 yn Exponenhial (a) (C) = 0. 80 Ply> 4000) 0.80 Pm 10.80) 4 000 Meon time Therefore, %3D 17925.68