M
  • M
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
Mathematics
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M
  • M
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
Mathematics
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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anonymous
  • anonymous
0%. Even if you get 3 of the heaviest mineral, it only gives you 270 lbs (unless you means something else)
M
  • M
answer is .0351 you may need to use linear combinations
anonymous
  • anonymous
What would be the constant? To you take out 1 mineral/mine or what?

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anonymous
  • anonymous
I think some info is missing.
M
  • M
no other information is given sorry
M
  • M
standard deviations 12, 14, 10 forgot crucial information!
anonymous
  • anonymous
I got .036 do you know about moment generating functions?
M
  • M
some what the e^tx thing?
anonymous
  • anonymous
yes it's the expected value of e^tx. Do you know the moment generating function for a normal random variable?
M
  • M
no but i can look it up
anonymous
  • anonymous
i can type it for you... \[M(t)=e^{\mu*t+\sigma^{2}t^{2}/2}\]
M
  • M
there's so many variations of formulas i can't retain them in my memory
anonymous
  • anonymous
that has mu as the mean and sigma as the standard deviation
M
  • M
i've seen that before but didn't actually had to solve any questions with it so far
M
  • M
do i use that formula?
anonymous
  • 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
  • M
you can just tell me what it is lol
anonymous
  • 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
  • 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
  • anonymous
do you know how to convert it?
M
  • M
what is standard normal? and i don't think we can use standard normal chart for this
anonymous
  • 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
  • M
yeah
anonymous
  • anonymous
ok so you have the variance and mean, so you know the pdf and you integrate from 283 to infinity
M
  • M
i use the standard pdf formula?
anonymous
  • anonymous
yes you can use that. It's kind of a mess though I usually use standard normal
anonymous
  • 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
  • M
hmm ok i'll have to play around with it for a while
M
  • M
no we've only used charts for z-score
M
  • M
everything else we just integrated or didn't use charts
anonymous
  • anonymous
yeah z score, thats standard normal
M
  • M
oh haha
anonymous
  • anonymous
you have mean and standard deviation so use the z score to find probability
M
  • M
i only knew it as table VI on pg 382 lol
anonymous
  • anonymous
haha
M
  • M
using the z = (x-m)/st.dev?
anonymous
  • anonymous
yeah that's it. stddev is sqrt( sum of the variances of each variable) mean is sum of the means
M
  • M
oh ok thanks. are you an actuary?
anonymous
  • anonymous
im a graduate student in math studying modern algebra. I just took a grad probability class last semester though.
M
  • M
ahh nice
anonymous
  • anonymous
are you in college?
M
  • M
no i graduated recently but taking some courses at local college
M
  • M
need it for grad school
anonymous
  • anonymous
are you taking a prob/stats class now? i noticed a bunch of your questions are from that topic
M
  • M
probability and stat is worse than multivariable calc for me
M
  • M
yeah
anonymous
  • anonymous
i like prob not stats. Did my answers to your other questions show up? Im not sure it worked.
M
  • M
yeah they did thanks. but haven't worked on them
M
  • M
but i have a good idea on how to solve them now though
anonymous
  • anonymous
good. well ill cya around the site I just found it and I think its fun. good luck with your probability.
M
  • M
thanks!!

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