The number of surface flaws m a plastic roll used in the int

The number of surface flaws m a plastic roll used in the interior of automobiles has a Poisson distribution with a mean of 0.05 flaw per square foot of plastic roll. Assume an automobile Interior contains 10 square feet of plastic roll. What is the probability that there are no surface flaws in an auto\'s interior? If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws? If 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws? When network cards are communicating, bits can occasionally be corrupted in transmission. Engineers have determined that the number of bits in error follows a Poisson distribution with mean of 3.2 bits/kb. What is the probability of 5 bits being in error during the transmission of 1kb? What is the probability of 8 bits being in error during the transmission of 2kb? What is the probability of no error in 3 kb?

Solution

3.

X:No. of surface flaws per square foot of plastic roll used in the interior of automobiles.

X~P(0.05)

X₁: No. of surface flaws in the interior of automobiles.

X₁~P(0.05*10)=P(0.5)

P[X₁=0]=0.606531

P[none of the 10 cars has any surface flaws]=(P[X₁=0])¹⁰ [since the events are independent.]

=0.0067380

P[atmost 1 car has any surface flaws among 10 cars]=P[no car has any flaw]+P[1 car has surface flaws]

=(P[X₁=0])¹⁰ +(P[X₁=0])⁹(1-P[X₁=0])

=0.0067380+0.0043711

=0.0111091

4.

(a) X₁:No. of bits in error during the transmission of 1kb

X₁~P(3.2)

P[X₁=5]=0.113979

(b) X₂:No. of bits in error during the transmission of 2kb

X₂~P(3.2*2)

P[X₂=8]=0.115994

(c)X₃:No. of bits in error during the transmission of 3kb

X₃~P(3.2*3)

P[X₃=0]=0.0000677