Math Is Fun Forum

teo

Member

Registered: 2007-08-04

Posts: 7

normal distibution

the mass of one bar of 'chocoladees' is known to follow a normal distribution with mean 71 grams and standard deviation 7 grams. the mass of a stick of 'lollipopees' is known to follow a normal distribution with means 57 grams and standard deviation 5 grams.

1) what is the probability that the mass of 4 randomly choosen 'lollipopees' execced thrice the mass of one bar of 'chocoladees' by less than 10 grams? ans: 0.155

5 'chocoladees' and 2 'lollipopees' are packed in a goodie bag A of mass 2g. the total mass (in grams) of this goodie bag is denoted by S.
3 'chocoladees' and 5 'lollipopees' are packed into goodie bag B of mass 2g. the total mass (in grams) of this goodie bag is denoted by T.

2) find the probability that the mass of goodie bag A differs from the mass of goodie bag B by less than ten grams.  ans: 0.162

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to take the first step is easy, to climb up the mountain is another matter.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: normal distibution

Say you have a random number generator that spits out numbers from 11 to 12 like 11.15, 11.99, 11.70, 11.01, etc...
The probability distribution is a flat horizontal line from 11.0 to 12.0,
not a normal distribution, because that is how the man-made
generator is designed, sound good?
Now, let's think about your problem of adding 4 of these reading together...
But stick to my simple flat distribution.
Your problem says 4 lollipopees are chosen, but what would
happen if just 2 numbers came out of this number
generator and for every pair of numbers that
came out, they were added together.
Now the range ofcourse would be from 22.0 to 24.0,
but the funny thing is ofcourse, is to wonder if the
probability distribution is still flat or not.
I have a hunch it is not flat because I think the things
will tend toward the middle when you add up a lot of them.
But I am doing no rigorous work here, it is
just speculation...

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: normal distibution

Actually, I think it is a triangle distribution.
Because if you hold one variable constant, and
change the other one, and do a double loop, now
allowing both variables to change, you get
a triangular summation graph if you use
distinct objects, I think.
Like from 22.0 to 23.0 the line slopes up, but
from 23.0 to 24.0, the line slopes down.
Anyone agree?

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igloo myrtilles fourmis