Question

Suppose that only 0.1% of all computers of a certain type experience CPU failure during the warranty period. Consider a sample of 2,000 computers.

(a) What are the expected value and standard deviation of the number of computers in the sample that have the defect? (Round your standard deviation to two decimal places.)

expected value	computers
standard deviation	computers

(b) What is the (approximate) probability that more than 4 sampled computers have the defect? (Round your answer to three decimal places.)


(c) What is the (approximate) probability that no sampled computers have the defect? (Round your answer to five decimal places.)

Answer 1

a)

mean of distribution=μ=np=

2.000

standard deviation σ=√(np(1-p))=

1.41

b)

this follows POisson distribution with parameter λ =2

probability that more than 4 sampled computers have the defect:

probability =

P(X>=5)=

1-P(X<=4)=

1-∑x=0x-1   {e-λ*λx/x!}=

0.053

c)

probability that no sampled computers have the defect:

probability =

P(X=0)=

{e-λ*λx/x!}=

0.13534