Hi, I'm looking through some past papers for an exam I have this weekend and have come across this strange binomial distribution question, that's very confusing.. Here it is:

A series of wall covering tiles is tested to determine the temperature at which a tile will ignite. The testing laboratory reports that the mean temperature is 290 degrees C, with a standard deviation of 40C. The testing lab also indicated that the data obtained follows a Gaussian distribution. The authorities require that no ignition should occur up to a temperature of 280C. Therefore, the owner of the building decides to conduct a full scale test where he imposes 280C on a square wall with 32 tiles. What is the probability that at least one will ignite?


What I've done so far is calculate the transformed value (to a standardised normal variate) - x-x(bar)/s = 280-290/40 = -0.25.

I then got P(X=0.25) from the table as 0.5987, but I'm really confused with all this stuff and don't know where to go from here, or even if I've got any of that stuff right.. Please help! :)

Steven,

Use a two-step process to solve this problem.

(1) From the given information, mean=290, sd=40, use the normal distribution to determine the probability that a given ignition temperature is 280 degrees or less. You should get z = -0.25, and the probability of z less than or equal to -0.25 is 0.4013.

(2) Use the probability found in (1) to set up the binomial formula....if the probability of 1 tile igniting at 280 deg is 0.4013, then what is the probability of 0 tiles out of 32 igniting?

Once you get the answer from step (2), subtract it from 1.0 to get your answer.

JohnM

So, then we have 32C0 0.4013^0*0.5987^32, which simplifies to just 0.5987^32, which gives a tiny number.. Meaning the probability that at least one ignites is 99.99999258?

That sounds a bit high, but I guess that 280 degrees was well within the 1 standard deviation, and quite close to the mean, so I suppose that's correct?

Thanks for your help.. It's been a long day today, and my brain's already fried from the exam I had this morning. Think I'm gonna give up for tonight.. taking nothing in at all..:shakehead

not .5987^32 but .4013^32

but they're both virtually 0, so yes, it's a virtual guarantee that at least 1 tile will ignite

Aah, of course.. As I said, I'm not on top form following all the thinking today ;)
Thanks again for your help! :)