Answer to Question #103465 in Statistics and Probability for Maow Abdullahi

Question

1a)A manufacturer assures his customers that the probability of having defective item is 0.005. A sample of 1000 items was inspected. Find the probabilities of having the following possible outcomes
i).Only one is defective
ii).At most 2 defective
iii) More than 3 defective

Answer 1

1. probability of having a defective item (p)= 0.005 => q=1-0.05=0.995

N=100;

This is a binomial distribution

P(X=x)=(nCx)*p^x*q^n-x

i)P (only one is defective)

p(X=1)= (1000C1)*0.005^1*0.995^999

=0.0334

ii) p( at most 2 defective)

p(X<=2)=p(X=0)+p(X=1)+p(X=2)

=(1000C0)*0.005^0*0.995^1000+(1000C1)*0.005^1*0.995^999+ (1000C2)*0.005^2*0.995^998

=0.1240

iii)p(more than 3 defective)

p(X>3)= 1-p(X<=3)

=1-( p(X=0)+p(X=1)+p(X=2)+p(X=3))

=1-((1000C0)*0.005^0*0.995^1000+ (1000C1)*0.005^1*0.995^999+ (1000C2)*0.005^2*0.995^998+ (1000C3)*0.005^3*0.995^997)

=1-0.2643

=0.7357