Question

ImprovingQuality:The Write RightCompany manufacturesballpoint pens and has been experiencing a 6% rate of defectivepens.Modifications are made to the manufacturing process inan attemptto improve quality, and the manager claims that themodified procedure is better, because a test of 60 pens shows thatonly one is defective.
a.Assuming that the 6% rate of defects hasnot changed, find the probability that among 60 pens, exactly oneis defective.
b.Assuming that the 6% rate of defects hasnot changed, find the probability that among 60 pens, none aredefective.
c.What probability valueshould be used for determining whether the modified process resultsin a defective rate that isless than 6%?
d.What do you conclude about theeffectiveness of the modified production process?

Answer 1

n= 60

p= 0.06

a)

p(exactly 1 is defective) = 60C1*(0.06)¹(1-0.06)⁵⁹ = 0.0935

B)  

P(NONE IS DEFECTIVE )

=60C0 *(0.06)⁰(1-0.06)⁶⁰ = 0.0244

c)

6% of pens = 60*0.06 = 3.6= 4(round value)

so now  

p(x<4) = p(3)+ p(2)+p(1)+p(0)

= 0.0244+0.0935+0.176+0.2173

=0.5133

d))

modified procedure is better