What is the probability of passing a shipment using a binomial distribution?

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Homework Statement

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?

Homework Equations

b(x;n,p) = (nCx) p^x(1-p)^(n-x)
μ = np

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?

 

[ehild]

Homework Statement

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?

Homework Equations

b(x;n,p) = (nCx) p^x(1-p)^(n-x)
μ = np

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?

Yes.

 

[toothpaste666]

thank you