Answer to Question #115751 in Statistics and Probability for Buzuah valtas

Question

The rate of defectiveness of items from a production line is 2% five items are randomly selected from the production line
a) present the probability distribution table .
b) At least two items are defective
c) At least two items are defective
d) Given that 100 items we're randomly selected instead, find the average number of defective items

Answer 1

n=5,p=0.02,q=1-0.02=0.98

a)

x-amount of defective items

P(x=0)=C_5,0*0.02⁰*0.98⁵=0.9039

P(x=1)=C_5,1*0.02^1*0.98⁴=0.0922

P(x=2)=C_5,2*0.02²*0.98³=0.0037

P(x=3)=C_5,3*0.02³*0.98²=7.683*10^-5

P(x=4)=C_5,4*0.02⁴*0.98=7.84*10^-7

P(x=5)=0.02⁵=3.2*10^-9

Table

Defective 0 1 2 3 4 5

P 0.9039 0.0922 0.0037 7.683*10^-5 7.84*10-7 3.2*10-9

b) At least two items are defective  

P(x≥2)=1-P(x=0)-P(x=1)=1-0.9039-0.0922=0.0039

c) At least two items are defective  

P(x≥2)=1-P(x=0)-P(x=1)=1-0.9039-0.0922=0.0039

d) μ=np=100*0.02=2