Question

Industrias Beltrán produces computer cards and contracts with a wide variety of clients. An acceptable quality level (NAC) of 6.5% has been established in a contract. That is, those batches with 6.5% or less are considered acceptable batches. Based on the previous NCA, Industrias Beltrán requires a sample of 13 cards for each selected lot. The lot is accepted or rejected according to the following decision rule:

Accept lot if R ≤ 2
Rejects batch if R> 2

Where R is the number of defective cards in the sample.

a) What is the probability of accepting a lot that has 20% defective?

b) What is the probability of rejecting a lot that has 2% defective?

Answer 1

a)

P(accepting the lot ) =P(R<=2 |p=0.2) =P(R=0)+P(R=1)+P(R=2)

=(13C0)*(0.20)⁰(0.8)¹³+(13C1)*(0.20)¹(0.8)¹²+(13C2)*(0.20)²(0.8)¹¹

=0.5017

b)

probability of rejecting a lot that has 2% defective =P(R>2 |p=0.02)=1-(P(R=0)+P(R=1)+P(R=2))

=1-((13C0)*(0.02)⁰(0.98)¹³+(13C1)*(0.02)¹(0.98)¹²+(13C2)*(0.02)²(0.98)¹¹ )

=1-0.9980

=0.0020