Question

A construction company buys screws in bulk. A new supplier approaches the company with an extremely low price, but acknowledges that they are still scaling up their production. Their most recent production run was 100,000 screws and data from their quality control process indicate that 0.3% of the screws have production faults.

a) What is the probability that a box of 1200 screws has exactly 1 faulty screw?

b) What is the probability that a small order of 4800 screws has fewer than 10 faulty

screws?

c) What is the probability that a larger order of 18000 screws has more than 100 faulty

screws?

Answer 1

a)

expected faulty screw =np=1200*0.3%=3.6

hence  probability that a box of 1200 screws has exactly 1 faulty screw =e^-3.6*3.6¹/1!=0.0984

b)

n=	4800	p=	0.0030
here mean of distribution=μ=np=		14.4
and standard deviation σ=sqrt(np(1-p))=		3.7890

probability that a small order of 4800 screws has fewer than 10 faulty screws:

probability =

P(X<9.5)

=

P(Z<-1.29)=

0.0985

c)

here mean of distribution=μ=np=		54
and standard deviation σ=sqrt(np(1-p))=		7.3374

probability that a larger order of 18000 screws has more than 100 faulty screws:

probability =

P(X>100.5)

=

P(Z>6.34)=

1-P(Z<6.34)=

1-1=

0.0000