Math Is Fun Forum

VCFan1001

Member

Registered: 2011-09-22

Posts: 3

I need help with this question experimental probability.

Hi, I was assigned math homework today and I  finished it but left one question blank. I don't like to leave questions blank so that is why I am here asking for help. The question is

#7 At a light bulb factory, a batch of bulbs is rejected if more than 5% of the bulbs in a sample taken from the batch are defective.

a, If 240 bulbs are tested and 8 are defective, will the batch be rejected? Show your calculation

b, in a batch of 1000 bulbs, exactly 100 are defective. A sample of 200 bulbs from the batch of 1000 is tested. Do you expect the batch will be defective? Explain your reasoning.

c, In a large batch of bulbs, 1% of the bulbs are defective. A sample of bulbs is tested. Is it possible that the entire batch will be rejected? Explain your reasoning

I have already completed a,b and got the correct answer but how would I do c. For c I wrote: No the bulbs will not be rejected because only 1% are defective and 1% does not surpass 5% so the batch will be kept, but in the back of the textbook it says the bulbs will be rejected. Can someone tell me how the bulbs will be rejected? Basically I just made an assumption that they would not be rejected because all I was given was 1%. Would I need to find the number of bulbs that are being tested? How would I do that.

The formula for experimental probability is: p(event)=number of successful trials/total number of trials

Last edited by VCFan1001 (2011-09-26 13:47:23)

VCFan1001

Member

Registered: 2011-09-22

Posts: 3

Re: I need help with this question experimental probability.

Should I elaborate on question a,b so you guys can get an example of what I did?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: I need help with this question experimental probability.

Hi VCFan1001;

Welcome to the forum.

The question seems a little bit unclear. This is how I understand it:

If it is known that in population of bulbs that 1% are defective it is possible that a sample taken from it could have higher than 5% defective bulbs. Conceivably they could all be defective. It will be rare but the probability is not 0.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: I need help with this question experimental probability.

hi VCFan1001

Reading the question I'm getting the impression that your teacher is working towards something called the 'binomial distribution' and then on to the 'normal distribution'.  Maybe you've got there already.

A 1% failure rate only means that a typical number of defectives is 1 in a hundred.  It doesn't mean that this will  be the proportion in an actual sample.  The number of failures in practice may be more or less than this.

The graph below shows what may be expected to happen in taking samples.  If you know the sample size it is possible to use the graph to calculate the chances of getting 2%, 3% 4% 5% etc of failures.  The graph 'tails off' either side of the theoretical rate of 1%,  so it becomes increasingly unlikely that a sample will have a rate that is far from the middle.

But it is not impossible.  The tails trail off to zero but never quite reach zero so it is possible that a sample could have a 5% failure rate.  When you have done the theory for this you'll be able to say how likely this is.

Bob

ps.  The main Maths Is Fun site has pages about the binomial distribution and the normal distribution if you are interested in reading ahead.

pps  Have a look at http://www.mathsisfun.com/data/quincunx.html  This shows how a theoretical rate of 50% (P=0.5) produces the typical bell shaped graph as the sample size increases.  You can vary the value of P, and speed up the 'flow rate'.

Although most balls fall down the middle, occasionally you will see a ball that favours the left or the right and ends up far from the middle.

ppps  What or who is VC that you are a fan.  I'm from the UK so I don't recognise the reference.  That also explains why I cannot spell favour.  Welcome to the Forum! 

Last edited by Bob (2011-09-26 19:29:15)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

VCFan1001

Member

Registered: 2011-09-22

Posts: 3

Re: I need help with this question experimental probability.

Thank you, that link you posted is very helpful. I will read up on it later since I'm tired. I just finished my math homework. Also I asked my teacher for help on the question I was having trouble with today, and she told me something similar to what you posted, but ill read up on the link to get a better understanding so when I see a similar question on a quiz,test or exam I will be able to answer it easily.

VC is short for Vince Carter he's a pro basketball player.

Last edited by VCFan1001 (2011-09-27 10:36:04)