When a new machine is functioning properly, only 3% of the items produced are de

ID: 3135333 • Letter: W

Question

When a new machine is functioning properly, only 3% of the items produced are de-

fective. Assume that we will randomly select four parts produced on the machine and

that we are interested in the number of defective parts found.

(a) Compute the probability of nding no defective parts.

(b) Compute the probability of nding exactly one defective part.

(d) Compute the probability of nding at most one defective part.

(e) Compute the expected number of defective parts found.

(f) Compute the variance of the number of defective parts.

(g) Compute the standard deviation of the number of defective parts

The random variable X=number of defective parts follows binomial with parameters n=4, p=0.03

(a)P(X=no defective)

=4C0*0.03^0*(1-0.03)^4

=0.88

(b)P(X=1)

=4C1*0.03^1*(1-0.03)^3

=0.109

(c)P(at least 1)=P(X>=1)

=4C1*0.03^1*(1-0.03)^3+…+4C4*0.03^4*(1-0.03)^0

=0.114

(d)P(at most 1)=P(X<=1)

=4C0*0.03^0*(1-0.03)^4+4C0*0.03^0*(1-0.03)^4

=0.994

(e)The expectation is: n*p=4*0.03=0.12

(f)The variance is np(1-p)=0.12*0.97=0.1164

(g)The standard deviation is root over np(1-p)=0.34

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