082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

960 Chapter 29 Statistics and probability distributions
( 250
(a) P(X =3) =
3
( 250
(b) P(X =7) =
7
Poissonprocess
)
(0.02) 3 (0.98) 247 = 0.140
)
(0.02) 7 (0.98) 243 = 0.105
Sincenislargeand pissmallthePoissondistributionwillbeagoodapproximation
tothe binomial distribution
λ=np=5
(a) P(X =3) = e−5 (5) 3
= 0.140 (b) P(X = 7) = e−5 (5) 7
= 0.104
3!
7!
EXERCISES29.11
1 Acomputer network has several hundredcomputers.
During an 8 hour period,thereare on averageseven
computers notfunctioning. Find the probabilitythat
duringan 8 hour period
(a) nine (b) five
donot function.
2 Aworkforce has on averagetwo people absent
through illnessonany given day. Find the probability
that onatypicalday
(a) two
(b) atleast three
(c) less thanfour
people are absent.
3 Amachine manufactures 300 micro-chips perhour.
Theprobability an individual chipis faultyis 0.01.
Calculate the probabilitythat
(a) two
(b) four
(c) more thanthree
faultychipsaremanufacturedinaparticularhour.Use
both the binomial andPoisson approximations and
comparethe resulting probabilities.
4 Theprobability ofadisk drive failurein any weekis
0.007. Acomputer servicecompany maintains900
disk drives.Usethe Poisson distribution to calculate
the probability of
(a) seven (b) more thanseven
disk drivefailures in a week.
5 Theprobability an employee fails to cometo work is
0.017. Alarge engineeringfirm employs650 people.
Whatisthe probability thatonaparticularday
(a) nine (b) 10
people are away from work?
6 Amachine manufactures electrical components for
the car industryatthe rate of750 per hour.The
probability acomponentis faultyis 0.013. Useboth
the binomialdistribution andthe corresponding
Poisson approximation to findthe probabilitythat in a
sampleof200 components
(a) none are faulty
(b) oneisfaulty
(c) two are faulty
(d) three are faulty
(e) more thanthree are faulty
Solutions
1 (a) 0.1014 (b) 0.1277
2 (a) 0.2707 (b) 0.3233
(c) 0.8571
3 (a) Binomial0.2244; Poisson 0.2240
(b) 0.1689,0.1680
(c) 0.353,0.353
4 (a) 0.1435 (b) 0.2983