Sick days

In Canada, there are typically 261 working days per year. If there is a 4.9% chance that an employee takes a sick day. ..
what is the probability an employee will use 17 OR MORE sick days in a year?

Correct result:

p =  0.0929

Solution:

q=4.9%=4.9100=0.049 n=261  C0(261)=(2610)=261!0!(2610)!=11=1  p0=(2610) q0 (1q)n0=1 0.0490 (10.049)26100 C1(261)=(2611)=261!1!(2611)!=2611=261  p1=(2611) q1 (1q)n1=261 0.0491 (10.049)26110 C2(261)=(2612)=261!2!(2612)!=26126021=33930  p2=(2612) q2 (1q)n2=33930 0.0492 (10.049)26120.0002 C3(261)=(2613)=261!3!(2613)!=261260259321=2929290  p3=(2613) q3 (1q)n3=2929290 0.0493 (10.049)26130.0008 C4(261)=(2614)=261!4!(2614)!=2612602592584321=188939205  p4=(2614) q4 (1q)n4=188939205 0.0494 (10.049)26140.0027 C5(261)=(2615)=261!5!(2615)!=26126025925825754321=9711475137  p5=(2615) q5 (1q)n5=9711475137 0.0495 (10.049)26150.0071 C6(261)=(2616)=261!6!(2616)!=261260259258257256654321=414356272512  p6=(2616) q6 (1q)n6=414356272512 0.0496 (10.049)26160.0157 C7(261)=(2617)=261!7!(2617)!=2612602592582572562557654321=15094407070080  p7=(2617) q7 (1q)n7=15094407070080 0.0497 (10.049)26170.0294 C8(261)=(2618)=261!8!(2618)!=26126025925825725625525487654321=479247424475040  p8=(2618) q8 (1q)n8=479247424475040 0.0498 (10.049)26180.0481 C9(261)=(2619)=261!9!(2619)!=261260259258257256255254253987654321=13472177599131680  p9=(2619) q9 (1q)n9=13472177599131680 0.0499 (10.049)26190.0696 C10(261)=(26110)=261!10!(26110)!=339498875498118336  p10=(26110) q10 (1q)n10=339498875498118336 0.04910 (10.049)261100.0904 C11(261)=(26111)=261!11!(26111)!=7746747068184336576  p11=(26111) q11 (1q)n11=7746747068184336576 0.04911 (10.049)261110.1063 C12(261)=(26112)=261!12!(26112)!1.613×1020=161390563920507012000  p12=(26112) q12 (1q)n12=161390563920507012000 0.04912 (10.049)261120.1141 C13(261)=(26113)=261!13!(26113)!3.091×1021=3091250032015865076000  p13=(26113) q13 (1q)n13=3091250032015865076000 0.04913 (10.049)261130.1126 C14(261)=(26114)=261!14!(26114)!5.475×1022=54759286281423895632000  p14=(26114) q14 (1q)n14=54759286281423895632000 0.04914 (10.049)261140.1028 C15(261)=(26115)=261!15!(26115)!9.017×1023=901702914100780148073600  p15=(26115) q15 (1q)n15=901702914100780148073600 0.04915 (10.049)261150.0872 C16(261)=(26116)=261!16!(26116)!1.386×1025=13863682304299494776631600  p16=(26116) q16 (1q)n16=13863682304299494776631600 0.04916 (10.049)261160.0691 C17(261)=(26117)=261!17!(26117)!1.998×1026=199800127326669189427926000  p17=(26117) q17 (1q)n17=199800127326669189427926000 0.04917 (10.049)261170.0513  s=p0+p1+p2+p3+p4+p5+p6+p7+p8+p9+p10+p11+p12+p13+p14+p15+p16+p17=0+0+0.0002+0.0008+0.0027+0.0071+0.0157+0.0294+0.0481+0.0696+0.0904+0.1063+0.1141+0.1126+0.1028+0.0872+0.0691+0.05130.9071 p=1s=10.9071=0.0929



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