Bernoulli distribution

The production of solar cells produces 2% of defective cells. Assume the cells are independent and that a lot contains 800 cells. Approximate the probability that less than 20 cells are defective. (Answer to the nearest 3 decimals).

Correct answer:

p =  0.814

Step-by-step explanation:

C0(800)=(0800)=0!(8000)!800!=11=1 C1(800)=(1800)=1!(8001)!800!=1800=800 C2(800)=(2800)=2!(8002)!800!=21800799=319600 C3(800)=(3800)=3!(8003)!800!=321800799798=85013600 C4(800)=(4800)=4!(8004)!800!=4321800799798797=16938959800 C5(800)=(5800)=5!(8005)!800!=54321800799798797796=2696682400160 C6(800)=(6800)=6!(8006)!800!=654321800799798797796795=357310418021200 C7(800)=(7800)=7!(8007)!800!=7654321800799798797796795794=40529210272690400 C8(800)=(8800)=8!(8008)!800!=87654321800799798797796795794793=4017457968280435900 C9(800)=(9800)=9!(8009)!800!3.535×1020=353536301208678359200 C10(800)=(10800)=10!(80010)!800!2.796×1022=27964721425606458212720 C11(800)=(11800)=11!(80011)!800!2.008×1024=2008375447839009271640800 C12(800)=(12800)=12!(80012)!800!1.320×1026=132050685695414859610382600 C13(800)=(13800)=13!(80013)!800!8.004×1027=8004303102152839182537037600 C14(800)=(14800)=14!(80014)!800!4.499×1029=449956181528163174046903470800 C15(800)=(15800)=15!(80015)!800!2.357×1031=23577703912075750320057741869920 C16(800)=(16800)=16!(80016)!800!1.156×1033=1156781098186216500077832960492950 C17(800)=(17800)=17!(80017)!800!5.334×1034=53348022410470219768295355354498400 C18(800)=(18800)=18!(80018)!800!2.320×1036=2320638974855454559920847957920680400 C19(800)=(19800)=19!(80019)!800!9.551×1037=95512614649313971887268584373366951200 q=2%=1002=0.02 n=800 d=20  p0=(0n) q0 (1q)n0=1 0.020 (10.02)80009.5689108 p1=(1n) q1 (1q)n1=800 0.021 (10.02)80011.5623106 p2=(2n) q2 (1q)n2=319600 0.022 (10.02)80021.2737105 p3=(3n) q3 (1q)n3=85013600 0.023 (10.02)80030.0001 p4=(4n) q4 (1q)n4=16938959800 0.024 (10.02)80040.0003 p5=(5n) q5 (1q)n5=2696682400160 0.025 (10.02)80050.0009 p6=(6n) q6 (1q)n6=357310418021200 0.026 (10.02)80060.0025 p7=(7n) q7 (1q)n7=40529210272690400 0.027 (10.02)80070.0057 p8=(8n) q8 (1q)n8=4017457968280435900 0.028 (10.02)80080.0116 p9=(9n) q9 (1q)n9=353536301208678359200 0.029 (10.02)80090.0208 p10=(10n) q10 (1q)n10=27964721425606458212720 0.0210 (10.02)800100.0335 p11=(11n) q11 (1q)n11=2008375447839009271640800 0.0211 (10.02)800110.0492 p12=(12n) q12 (1q)n12=132050685695414859610382600 0.0212 (10.02)800120.066 p13=(13n) q13 (1q)n13=8004303102152839182537037600 0.0213 (10.02)800130.0816 p14=(14n) q14 (1q)n14=449956181528163174046903470800 0.0214 (10.02)800140.0936 p15=(15n) q15 (1q)n15=23577703912075750320057741869920 0.0215 (10.02)800150.1001 p16=(16n) q16 (1q)n16=1156781098186216500077832960492950 0.0216 (10.02)800160.1002 p17=(17n) q17 (1q)n17=53348022410470219768295355354498400 0.0217 (10.02)800170.0943 p18=(18n) q18 (1q)n18=2320638974855454559920847957920680400 0.0218 (10.02)800180.0837 p19=(19n) q19 (1q)n19=95512614649313971887268584373366951200 0.0219 (10.02)800190.0703  p=p0+p1+p2+p3+p4+p5+p6+p7+p8+p9+p10+p11+p12+p13+p14+p15+p16+p17+p18+p19=9.5689108+1.5623106+1.2737105+0.0001+0.0003+0.0009+0.0025+0.0057+0.0116+0.0208+0.0335+0.0492+0.066+0.0816+0.0936+0.1001+0.1002+0.0943+0.0837+0.0703=0.814



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