Respuesta :
Answer:
(a) The probability of that the lot will be rejected is 0.1904.
(b)The probability of that the lot will be rejected is 0.5315 .
(c)The probability of that the lot will be rejected is 0.7026.
Step-by-step explanation:
The formula of Hypergeometric distribution is
[tex]P(X=x)=\frac{(^{R}C_x)( ^{N-R}C_{n-x})}{^NC_n}[/tex]
N= number of population
R= The number of success event
n= sample of size
(a)
Given that, N= 60, R=5 and n=10
More than 1 is defected, the lot will be rejected.
X is random variable and defined the number of rejected item.
P(X>1)=1-P(X≤1)
=1 - P(X=0) - P(X=1)
[tex]=1- \frac{(^5C_0)(^{60-5}C_{10-0})}{^{60}C_{10}}-\frac{(^5C_1)(^{60-5}C_{10-1})}{^{60}C_{10}}[/tex]
=1 - 0.3879 - 0.4217
=0.1904
The probability of that the lot will be rejected is 0.1904.
(b)
N= 60, R=10 and n=10
X is random variable and defined the number of rejected item.
P(X>1)=1-P(X≤1)
=1 - P(X=0) - P(X=1)
[tex]=1- \frac{(^{10}C_0)(^{60-10}C_{10-0})}{^{60}C_{10}}-\frac{(^{10}C_1)(^{60-10}C_{10-1})}{^{60}C_{10}}[/tex]
=1-0.1362-0.3323
=0.5315
The probability of that the lot will be rejected is 0.5315 .
(c)
N= 60, R=20 and n=10
X is random variable and defined the number of rejected item.
P(X>1)=1-P(X≤1)
=1 - P(X=0) - P(X=1)
[tex]=1- \frac{(^{20}C_0)(^{60-20}C_{10-0})}{^{60}C_{10}}-\frac{(^{20}C_1)(^{60-20}C_{10-1})}{^{60}C_{10}}[/tex]
=1 -0.2249 - 0.0725
=0.7026
The probability of that the lot will be rejected is 0.7026.
