Question on probabilty

#1 10-29-2002, 04:07 PM

Cant figure out this question. Need some help. An automaticf machine in a manufacturing process is operating properly if the lenghts of an important subcompent are normally distributed with a mean of 117 cm and standard deviation of 5.2 cm. FIND the probabilty that if four subcomponents are randomly selected, all four have lengths that exceed 120 cm. If you konw how to do by excel, that would work also. Thanks a ton

Homer · #2 10-29-2002, 04:14 PM

Please do not cross-post these problems. Also, if you expect us to do your homework for you, you should pay us...

#3 10-29-2002, 05:48 PM

I'm not going to do homework for you... I'll give you some hints. Note: I'm not claiming what I'm about to say is correct. If it is, great. If not... hey, you get what you pay for.

I believe you need to find the Z-value that corresponds to the 0.577 std. dev. From this Z-value you should be able to arrive at a probability that any random part is > 120 cm. From this probability, you should be able to figure out the probability of 4 random parts > 120 cm.

PseudoPserious · #4 10-29-2002, 08:12 PM

Are you the same Needhelpfast who asked a homework question about spinning a roulette wheel a few weeks back, then didn't bother to say 'thank you' to those who responded?

PP

#5 10-30-2002, 12:55 PM

P(single item above mean) = .5
You want this to happen four times and are assuming independence. apply probability rules for independent events.

PseudoPserious · #6 10-30-2002, 01:24 PM

He's looking for 4 items above 120 cm, not the mean of 117 cm.

Also, I disagree that
P(single item above mean) = .5

For some distributions like the normal, then yes, it's true, but not for distributions in general.

For example, let's say that 99 rods are 1 cm long and 1 rod is 101 cm long. The mean length is 2 cm, but P(longer than the mean) = 0.01, not 0.5.

PP

#7 10-30-2002, 02:02 PM

If you have mean and std dev you approach the problem one way, if you have the population listed you approach it another

#8 10-30-2002, 03:03 PM

This is "Anonymous" who wrote the first response (not the other Anonymous)... You're totally right, P( > Mean ) does not necessarily = .5, just as you've shown.

The question posed said the subcomponents were normally distributed. It gave a mean and a std. dev. I'm posting again, because I would like to find out the correct method to solve this.

I proposed my approach, and I'd like to know if it is wrong (about using a lookup table to find the z-value for 3/5.2 = .577. Then, using the looked-up z-value figure out the P( > 120 cm ). From there it is straightforward...

Any comments? I'm not that sure my method would yield the correct answer? Does anyone know for sure?

Homer · #9 10-30-2002, 03:17 PM

Yes, it yields the correct answer. Find the probability of one being above 120cm (using the z chart), then take that to the 4th power.

-- Homer

PseudoPserious · #10 10-30-2002, 05:29 PM

Your method = a very good approach.

I think the only better approach would be to construct such a machine and randomly select 4 rods, oh, a couple of thousand times and thus experimentally determine the probability. That way if you're not good at reading charts, it eliminates that as a potential source of error.

PP