minerals produced from mines 1, 2, 3 and are independent normal random variables with means 80, 90, 75 pounds, respectively. what is the probability that the combined amount of mineral produced from all three mines exceeds 283 pounds? [Hint: use sum random variable Y = X1 + X2 + X3

- M

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- anonymous

0%. Even if you get 3 of the heaviest mineral, it only gives you 270 lbs (unless you means something else)

- M

answer is .0351
you may need to use linear combinations

- anonymous

What would be the constant? To you take out 1 mineral/mine or what?

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## More answers

- anonymous

I think some info is missing.

- M

no other information is given sorry

- M

standard deviations 12, 14, 10
forgot crucial information!

- anonymous

I got .036 do you know about moment generating functions?

- M

some what
the e^tx thing?

- anonymous

yes it's the expected value of e^tx. Do you know the moment generating function for a normal random variable?

- M

no but i can look it up

- anonymous

i can type it for you...
\[M(t)=e^{\mu*t+\sigma^{2}t^{2}/2}\]

- M

there's so many variations of formulas i can't retain them in my memory

- anonymous

that has mu as the mean and sigma as the standard deviation

- M

i've seen that before but didn't actually had to solve any questions with it so far

- M

do i use that formula?

- anonymous

you use it to derive something that is helpful to remember about sum of independent normal vars. Do you want me to derive the result or just tell you what it is?

- M

you can just tell me what it is lol

- anonymous

ok haha. The mean of the sum of independent normal vars is the sum of the means, and the variance is the sum of the variances. So we have mean 80+90+75=245 and variance = 144+196+100=440

- anonymous

then you convert it to standard normal and find the probability of being greater than 283 by looking a a standard normal chart

- anonymous

do you know how to convert it?

- M

what is standard normal? and i don't think we can use standard normal chart for this

- anonymous

standard normal is normal with mean 0 variance 1. Well if you can't use the chart you just integrate. Do you know the pdf for normal variables?

- M

yeah

- anonymous

ok so you have the variance and mean, so you know the pdf and you integrate from 283 to infinity

- M

i use the standard pdf formula?

- anonymous

yes you can use that. It's kind of a mess though I usually use standard normal

- anonymous

im looking at the integral now its pretty bad. I think I'd have to do it numerically. You haven't used standard normal in your class before?

- M

hmm ok i'll have to play around with it for a while

- M

no we've only used charts for z-score

- M

everything else we just integrated or didn't use charts

- anonymous

yeah z score, thats standard normal

- M

oh haha

- anonymous

you have mean and standard deviation so use the z score to find probability

- M

i only knew it as table VI on pg 382 lol

- anonymous

haha

- M

using the z = (x-m)/st.dev?

- anonymous

yeah that's it. stddev is sqrt( sum of the variances of each variable) mean is sum of the means

- M

oh ok thanks. are you an actuary?

- anonymous

im a graduate student in math studying modern algebra. I just took a grad probability class last semester though.

- M

ahh nice

- anonymous

are you in college?

- M

no i graduated recently but taking some courses at local college

- M

need it for grad school

- anonymous

are you taking a prob/stats class now? i noticed a bunch of your questions are from that topic

- M

probability and stat is worse than multivariable calc for me

- M

yeah

- anonymous

i like prob not stats. Did my answers to your other questions show up? Im not sure it worked.

- M

yeah they did thanks. but haven't worked on them

- M

but i have a good idea on how to solve them now though

- anonymous

good. well ill cya around the site I just found it and I think its fun. good luck with your probability.

- M

thanks!!

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