t Burgac alarm system has ten io) fal serfe one ysf each falma is o.bo nomal app

Question

t Burgac alarm system has ten io) fal serfe one ysf each falma is o.bo nomal approximaton to the Binsmlal Distriethon )Te-percentage-t-t m en (en 25 ters roger who haye at least some college' educatnis a random sanpie of 30o Americans ear aud old and oider hnd the man 15 ru ec have at leastSome, coet edueshon Lea an 3 A Shu scor we 36the steand urs deviation of the pospuhen arfnd he15% confidene intuval of the mean scer the mean odt seede tnet ermnate the rhlizer-f the manuteeturer!went t2.ae99% 50 e t ha mythe true mean, standard de e hong and correct shimectrd to within 0012,hos ma c the experiment 2 nelzs/

Explanation / Answer

1)

no of components i.e n = 10

proability of each faling i.e p = 0.60

forlmula of Bionolial distribution P(X=r) = nCrpr(1-p)n-r

a)

probabilty that exactly six fails =  10C60.606(1-0.60)10-6 = 0.2508

b)

probabilty that atmost eight will fail = 1 - P(9) -P(10)

=  1- 10C90.609(1-0.60)10-9 -  10C100.6010(1-0.60)10-10

= 0.9536

c) none will fail = P(X=0) = 10C00.600(1-0.60)10 = 0.0001

d)

mean of normal approximation = np = 10*0.60 = 6

variance = 10*0.06*(1-0.60) = 2.4

standard devation = variance = 2.4 = 1.5492

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