central limit theorem

[david]

The central limit theorem can be used to analyze round-off error. Suppose that the round-off error on one number is represented as a uniform random variable on [−0.5,0.5]. If 100 different numbers are added, find the probability that the total round-off error exceeds 1, 2, and 5

 

[Deleted member 4993]

The central limit theorem can be used to analyze round-off error. Suppose that the round-off error on one number is represented as a uniform random variable on [−0.5,0.5]. If 100 different numbers are added, find the probability that the total round-off error exceeds 1, 2, and 5

The central limit theorem states that

the sum of a large number of independent observations from the same distribution has, under certain general conditions, an approximate normal distribution.

Now continue....

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[david]

well, so far i got

f(x)= 1/(0.5+0.5)=1

variance=1/12

mean=0

i think i need to use this equation Z=(x-mean)/square root variance

i don't know what i should do next

 

[Deleted member 4993]

well, so far i got

f(x)= 1/(0.5+0.5)=1

variance=1/12

mean=0

i think i need to use this equation Z=(x-mean)/square root variance

i don't know what i should do next

Calculate the z-values for the given situations.

 

[david]

Z=(1-0)/.289=3.46

Z=(2-0)/.289=6.928

Z=(5-0)/.289=17.321

i don't think this is right, is z values supposed to be this high