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WHO LIKES MATH? (Help needed, please)
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| Irishaddict |
So guys, my ever-entrepreneurial mother is currently pursuing her MBA part time and one of the required courses is Statistics. She has an assignment due on Tuesday morning (50 questions). We have finished 47 of them and I can't take it anymore. I'm not in school for freaking math.
I post the last 3 questions here in the hopes that one of you is just brilliant brilliant and comes to the answer with much more ease and grace than either of us is demonstrating at the present moment.
Drinks are on me (after I extract a fee from her) for anyone willing to help out. :)
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1. A normal distribution has a mean of 80 and a standard deviation of 14. Determine the value above which 80 percent of the values will occur.
2. Assume a binomial probability distribution with n=40 and pi=.55. Compute the following:
a) the mean and standard deviation of the random variable.
b) the probability that x is 25 or greater.
c) the probability that x is 15 or less.
d) the probability that x is between 15 and 25 inclusive.
3. Two-litre plastic bottles used for bottling cola are shipped in lots of 100. Suppose the lots are 5 percent defective. Some bottles leak, some are too small, and so forth.
a) In the sample of 100, how many of the bottles contains 8 or more defectives?
b) Tell why this situation meets the binomial assumptions.
c) What is the probability that a shipment of plastic bottles contains 8 or more defectives?
d) What is the probability that 8 and 10 bottles are defectives?
e) What is the probability that there are exactly 8 defectives?
f) What is the probability that there are no defectives? |
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| NuERA |
| wow daughter of the year. |
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| Cosmic Fur |
If you asked me this last year, I would have been able to give you the answers withing a few minutes. Alas, a year passed, so now I forgot all this .
Besides, I have enough of my own schoolwork to catch up on.
And why are you doing your mom's assignments anyway? My parents never did my assignments for me.... |
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| Irishaddict |
| quote: | Originally posted by Cosmic Fur
And why are you doing your mom's assignments anyway? My parents never did my assignments for me.... |
My parents have done plenty for me. Sue me for trying to return the favour. |
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| Jer. |
| quote: | Originally posted by NuERA
wow daughter of the year. |
Hear hear. |
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| Euphorica |
1. PVD
2.
a) PVD
b) PVD
c) PVD
d) PVD
3.
a) PVD
b) PVD
c) PVD
d) PVD
e) PVD
f) PVD |
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| DJ_Science |
I hope this makes sense...
> 1. A normal distribution has a mean of 80 and a standard deviation
> of 14. Determine the value above which 80 percent of the values will > occur.
You need a table for this one. Its about 68.3. Basically you want to look at z&sigma for which a one tailed test gives 20 percent outside. They key to this is a one tailed test. then &mu - z&sigma is the value above which 80% will fall.
> 2. Assume a binomial probability distribution with n=40 and p=.55.
> Compute the following:
> a) the mean and standard deviation of the random variable.
mean = &mu = n*pi
&sigma^2 = n*p*q = n*p*(1-p)
> b) the probability that x is 25 or greater.
You have to add a bunch of terms
P(x >= 25) = sum{n=25 to 40} {40!/[(n!)(15!)]}(0.55)^n(0.45)^(40-n)
= 0.2142
> c) the probability that x is 15 or less.
See "b", just sum from 0 to 15, P(x <= 15) = 0.0196
> d) the probability that x is between 15 and 25 inclusive.
P(15 <= x <= 25) = 0.8588 Again, same as above, just sum from 15 to 25.
> 3. Two-litre plastic bottles used for bottling cola are shipped in
> lots of 100. Suppose the lots are 5 percent defective. Some bottles > leak, some are too small, and so forth.
> a) In the sample of 100, how many of the bottles contains 8 or more > defectives?
They have essentially told you the mean is 5 or the probability of
the bottle being bad is 5% (mu = N*P, N = 100 => P = 0.05%).
You can use the diff. of the binomial from here on with P = 0.05.
(There i am defining a pass as a broken bottle).
P(8 or more) = 1 - P(7 or less)
= 1 - sum(n=0,7) [(100!/(n!*(100-n)!)](0.05)^0.05(0.95)^0.95
= 0.2340
> b) Tell why this situation meets the binomial assumptions.
Its a pass/fail test. Either the bottle has a defect or not. In
these cases, you want a distribution that is binary in nature, ie
the binomial.
> c) What is the probability that a shipment of plastic bottles
> contains 8 or more defectives?
Isn't this the same as a?
> d) What is the probability that 8 and 10 bottles are defectives?
at the Prob for 8 and 10 only, P = 0.08158677208886
> e) What is the probability that there are exactly 8 defectives?
0.10602553736479 same as above, but only the n = 8 term counts
> f) What is the probability that there are no defectives?
0.00592052922033 n = 0 term only |
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| Aitizaz |
this is for question 2 as its the easiest of the lot...lol. also im assuming thats a typo..instead of pi=.55 it should be p=.55 meaning the probability of x is 0.55
a) mean=np=40x0.55=22
st. dev.= sq. root of variance= sq root of np(1-p)=3.146
b)P{x>=25] = P[x=25] + P[x=26] + ... + P[x=40]
use the binomial formula...should be in your moms notes...
c)P[x<=15] = P[x=0] + ... + P[x=15]
same formula as b
d)P[15 >= x >= 25] = P[x=15] + ... + P[x=25]
same as above
EDIT: the above post occurred as i was typing this...i guess iw ont have to attempt 1 and 3 after all...hehe |
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| Irishaddict |
| quote: | Originally posted by DJ_Science
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| quote: | Originally posted by Aitizaz
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<3 |
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| Aitizaz |
to DJ_Science:
dude isnt standard dev. the sq root of the variance? |
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| Aitizaz |
| quote: | Originally posted by Irishaddict
<3 |
huh? |
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| Irishaddict |
| quote: | Originally posted by Aitizaz
huh? |
lol it's a heart, I'm saying thank-you :p |
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