# Probability of success

• Nov 3rd 2009, 03:29 PM
cechmanek32
Probability of success
Hi,

I think I know how to begin the setup of this problem, but I'm not really sure how to calculate anything. Here is the problem along with what I have figured out so far:

A pharmaceutical company receives a large shipment of aspirin tablets. The acceptance sampling plan is to randomly select and test 15 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted? (Round the three decimal places as needed).

I think I need to find n, p, and q. I believe n=number of tablets (15), p= the failure rate (.05) and q=non-failure rate (.95). Am I correct with these numbers? If so, how do I use them to compute the probability? That is where I'm confused.

Thank you so much for your help!!!!
• Nov 3rd 2009, 09:35 PM
Guess992
It sounds like they want you to use the hypergeometric formula.

$\displaystyle \frac{\binom{k}{x}\binom{N-k}{n-x}}{\binom{N}{n}}$

Where:
k = successes in population
x = successes you are looking for {0, 1}
N = population
n = sample
• Nov 3rd 2009, 10:10 PM
mr fantastic
Quote:

Originally Posted by cechmanek32
Hi,

I think I know how to begin the setup of this problem, but I'm not really sure how to calculate anything. Here is the problem along with what I have figured out so far:

A pharmaceutical company receives a large shipment of aspirin tablets. The acceptance sampling plan is to randomly select and test 15 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted? (Round the three decimal places as needed).

I think I need to find n, p, and q. I believe n=number of tablets (15), p= the failure rate (.05) and q=non-failure rate (.95). Am I correct with these numbers? If so, how do I use them to compute the probability? That is where I'm confused.

Thank you so much for your help!!!!

You are correct.

Let X be the random variable 'number of defective tablets'.

X ~ Binomial(n = 15, p = 0.05).

Calculate $\displaystyle \Pr(X \leq 1)$.

Using the binomial distribution is OK here because you're told that the population is large (thousands of tablets) and so it's essentially a sampling with replacement problem.
• Nov 4th 2009, 01:48 PM
cechmanek32
Thank you so much, I got it!!!!

(Smile)