A factory employs 7 workers on the day shift and 6 workers on the evening shift.
ID: 3172716 • Letter: A
Question
A factory employs 7 workers on the day shift and 6 workers on the evening shift. The QA guys select 4 workers (without replacement) from the 12 workers for an interview. Let the RV X=number of day workers selected in the sample. a). Calculate the pmf of X. b). Calculate the experted value and the variance of X. c). The QA guys hop on a plane to China and visit a factory with 1200 workers. 700 work the day shift and 500 work the evening shift. They again select 4 for interviews. Let Y=number of day workers selected in the sample. Calculate the experted value and teh variance of Y. Compare your answer to part b.
Explanation / Answer
a. The elementary events and corresponding values of X are as follows:
Where, E denotes evening shift and D denotes day shift.
Therefore, the p.m.f is as follows:
The properties of p.m.f is satisfied, that are
0<=P(X=x)<=1 and sigma P(x)=1.01~1
b. E(X)=mu=Sigma x*P(x)=0*0.07+1*0.29+2*0.29+3*0.29+4*0.07=2.02
Var(X)=Sigma P(x)*(x-mu)^2=0.07(0-2.02)^2+0.29(1-2.02)^2+0.29(2-2.02)^2+0.29(3-2.02)^2+0.07(4-2.02)^2
=1.14
Events Value of X EEEE 0 EEED 1 DEEE 1 EEDE 1 EDEE 1 EEDD 2 DDEE 2 DEED 2 EDDE 2 EDDD 3 DDDE 3 DEDD 3 DDED 3 DDDD 4Related Questions
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