# Homework Help: Binomial distribution problem

1. Oct 18, 2015

### toothpaste666

1. The problem statement, all variables and given/known data

A company is interested in evaluating its current inspection procedure on large shipments of identical items. The procedure is to take a sample of 5 items and pass the shipment if no more than 1 item is found to be defective. It is known that items are defective at a 10% rate overall.

(a) What proportion of shipments will be accepted, i.e., what is the probability that the inspection procedure will pass the shipment?

(b) What is the expected number of defectives in a sample of 5?

2. Relevant equations
b(x;n,p) = (nCx) p^x(1-p)^(n-x)
μ = np

3. The attempt at a solution
This is practice for a test and we won't have access to the tables so I need to do this with the formula
for part a) we are looking for the probability that 0 or 1 item is defective
this will be
b(0;5,.1)+b(1;5,.1)
= (5C0)(.1)^0 (.9)^5 + (5C1)(.1)^1(.9)^4
= .9^5 + 5(.1)(.9)^4
= .59049 + .32805
= .91854

b) μ = np = 5(.1) = .5

Am I doing this problem correctly?

2. Oct 18, 2015

### ehild

Yes.

3. Oct 18, 2015

thank you