# Stats/Prop question regarding sample sets

• Feb 2nd 2009, 05:22 PM
{solved}Stats/Prop question regarding sample sets
The problem is:

A machine cuts circular filters from large rolls of material. If 7.3% of the filters fail to meet the specifications, use the normal approximation to the binomial to compute the probability that a sample of 100 of the filters will contain 5 or fewer that fail to meet specifications.

1) Can anyone put this in dummy terms for me, and

2) Whats the answer and how did you get it?

Thanks
• Feb 2nd 2009, 05:30 PM
mathhomework
A machine cuts circular filters from large rolls of material. If 7.3% of the filters fail to meet the specifications, use the normal approximation to the binomial to compute the probability that a sample of 100 of the filters will contain 5 or fewer that fail to meet specifications.

1. sameple space is 100 and 7.3% fails, the failing filters are about 7.3 for every 100 filters.

2. The probability of having less than 5 failing filters is impossible because we already know that for every 100, at least 7.3 filters fail to meet the specification.

p(5 or less)=0
• Feb 3rd 2009, 04:10 AM
mr fantastic
Quote:

Originally Posted by mathhomework
A machine cuts circular filters from large rolls of material. If 7.3% of the filters fail to meet the specifications, use the normal approximation to the binomial to compute the probability that a sample of 100 of the filters will contain 5 or fewer that fail to meet specifications.

1. sameple space is 100 and 7.3% fails, the failing filters are about 7.3 for every 100 filters.

2. The probability of having less than 5 failing filters is impossible because we already know that for every 100, at least 7.3 filters fail to meet the specification.

p(5 or less)=0

This is wrong.

Let X be the random variable Number of filters that fail to meet specifications.

X ~ Binomial(n = 100, p = 0.073)

Note: "7.3% of filters fail to meet the specifications" means that p = 0.073.

You have to calculate $\displaystyle Pr(X \leq 5)$ using the normal approximation to the binomial distribution.

Now read 5.2 of this: Binomial distribution - Wikipedia, the free encyclopedia