The acceptable quality level for a lot of 100 pencils is 5% defective printing o

Question

The acceptable quality level for a lot of 100 pencils is 5% defective printing on them. Lot A contains 95 with clear printing and 5 with partial printing. A random lot of 15 pencils will determine if the lot is accepted. The sampling plan was revised to a sample size of 30, and a the following to be determined: Case 1- what is the probability of no defects in the sample Case 2- what is the probability that there is exactly 1 defect in the sample Case 3- what is the probability that there are exactly 3 defects in the sample

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a.
P( X = 0 ) = ( 30 0 ) * ( 0.05^0) * ( 1 - 0.05 )^30
= 0.2146

b.
P( X = 1 ) = ( 30 1 ) * ( 0.05^1) * ( 1 - 0.05 )^29
= 0.3389

c.
P( X = 3 ) = ( 30 3 ) * ( 0.05^3) * ( 1 - 0.05 )^27
= 0.127

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.