In a smartphone manufacturing plant a quality control engineer inspects each bat
ID: 3232000 • Letter: I
Question
In a smartphone manufacturing plant a quality control engineer inspects each batch of phones produced for defects. Suppose a particular batch contains 20 phones and 4 of them are defective. The engineer takes a sample of 3 phones from the batch and examines them for defects. If X is the number of defective phones he finds:
(a) What probability distribution does X follow?
(b) What is the most likely number of defective phones he will find?
(c) Calculate IE(X) and V ar(X).
Suppose the engineer independently inspects two more batches of size 25. Each of these batches contain 3 faulty phones. The engineer takes a sample of size 4 from each of these larger batches.
(d) How many faulty phones would you expect him to find in total between the 3 batches.
(e) What is the variance of the total number of faulty phones he finds?
Explanation / Answer
a) this is hypergeometricx distribution
b) most likely number =nK/N =3*4/20=12/20=0.6
c) E(X) =0.6
Var(X) =nk/N(1-k/N)(N-n)/(N-1) =3*4/20(1-4/20)*(20-3)/(20-1)=0.4295
2) total expected number =3*0.6=1.8
variance =3*0.4295=1.2884