Question

A manager at a company that manufactures cell phones has noticed that the number of faulty cell phones in a production run of cell phones is usually small and that the quality of one day's run seems to have no bearing on the next day. 

a) What model might you use to model the number of faulty cell phones produced in one day? 

b) of the mean number of faulty cell phones is 3.3 per day, what is the probability that no faulty cell phones will be produced tomorrow? 

c) If the mean number of faulty cell phones is 3.3 per day, what is the probability that 3 or more faulty cell phones were produced in today's run? 

a) Which model might you use? 

• Poisson 

• Geometric 

• Binomial 

• Uniform 

b) The probability that no faulty cell phones will be produced tomorrow is _______ 

Answer 1

b)

poisson probability distribution

P(X=x) = e-λλx/x!

λ = 3.3

P ( X =    0   ) = e^-3.3*3.3^0/0!=   0.0369

c)

P(X≥3) = 1 - P(X=0) - P(X=1) - P(X=2)

P ( X =    1   ) = e^-3.3*3.3^1/1!=   0.1217
P ( X =    2   ) = e^-3.3*3.3^2/2!=   0.2008

P(X≥3) = 1 - P(X=0) - P(X=1) - P(X=2 = 1 - 0.0369-0.1217-0.2008=  0.6406

Answer 2

Research has shown that about 2% of all products produced by BVH Company are defective. A quality inspector has just sampled 300 products from this company. Using the Poisson distribution, what is the probability that: Page 3 of4 (a) exactly 12 of them are defective? (b) at least 8 ofthem are defective?