徵求統計高手,2題問題!! - 羽球

1.若羽球生產過程中,不良率為0.04,品管者每一小時抽樣30顆檢驗,試問:
(A)抽到的樣本中無不良品之機率?
Poison分配解
λ=30*0.04=1.2
f(X)=(1.2^X)*e^(-1.2)/X!
f(0)=2.71828^(-1.2)=0.301194455 #
二項分配解
=0.96^30=0.293857643
(B)有一顆不良品之機率?
Poison分配解
f(1)=1.2*2.71828^(-1.2)=0.361433346
二項分配解
=30*0.04*0.96^29=0.367322054
2.7-11光臨人數是Poison分配,每5分鐘平均有2位顧客,試問:
(A)半小時內無顧客之機率?
λ=2*6=12
f(X)=(12^X)*e^(-12)/X!
f(0)=2.71828^(-12)
=0.00000614426194858204
(B)半小時內有10位以上顧客之機率?
以常態分配求近似機率
X~N(12,12)
P(X>10)連續校正
P(X>9.5)
P(Z > (9.5-12)/12^0.5 )
P(Z > -0.72)
=0.7642
泊松土法練鋼
=1-f(0~9)
=1-0.242394118
=0.757605882
f(0)=2.71828^(-12)
f(1)=12*2.71828^(-12)
f(2)=(12^2)/2*2.71828^(-12)
f(3)=(12^3)/(3*2)*2.71828^(-12)
f(4)=(12^4)/(4*3*2)*2.71828^(-12)
f(5)=(12^5)/(5*4*3*2)*2.71828^(-12)
f(6)=(12^6)/(6*5*4*3*2)*2.71828^(-12)
f(7)=(12^7)/(7*6*5*4*3*2)*2.71828^(-12)
f(8)=(12^8)/(8*7*6*5*4*3*2)*2.71828^(-12)
f(9)=(12^9)/(9*8*7*6*5*4*3*2)*2.71828^(-12)