Please help with the following question

[ttam10]

A firm produces chains. The length of each link is independent of each other
and normally distributed. The mean length of a link is 10. 95% of all links have a length
between 9 and 11. The total length of each chain is the sum of the lengths of its links. You
consider chains with 100 links

2. How probable is it that such a chain has a total length between 900 and 1100? Answer is 1, but I don't understand the reasoning behind it
3. How probable is it that such a chain has a total length between 990 and 1010?
4. How probable is it that such a chain has a total length between 999 and 1001?

 

[ondansetron]

How do you think the problem can be approached? We're happy to help with homework when an attempt is made.
Let's start basic: if you only had ONE (1) link, then what is the probability it's length is between 9 and 11? Between 9.9 and 10.1?

There are many ways to approach the problem, by the way.

 

[ttam10]

Is the probability between just 95% for chains between 9 and 11?
I'm not sure how to approach without standard deviation.

 

[Dason]

Hint: start by using the info provided to figure out the standard deviation for one link

 

[ttam10]

.51 = s.d

 

[Dason]

Do you know how to find the distribution of the sum of normally distributed random variables

 

[ttam10]

Yes, here are my answers for the first two questions:
2. How probable is it that such a chain has a total length between 900 and 1100? .95
3. How probable is it that such a chain has a total length between 990 and 1010? .0796

 

[Dason]

Not quite. What are you using for the distribution of the sum

 

[ttam10]

Can you please provide the formula?

I just used the z-score of 1.96 for a 99% confidence interval to calculate the standard deviation, then used that to solve for the subsequent z-score and associated p-values.

 

[Con-Tester]

First, read here on the basics of how to combine normally distributed random variables. Next, figure out how to apply such a combination to the problem at hand. (Hint: The mean length μ is the same for each link, as is the standard deviation σ.)

Finally, you can use this normal distribution calculator to compute the answers.

 

[ttam10]

Okay, thank you. Is my calculation of the standard deviation above correct?

 

[Con-Tester]

Yes, σ = 0.51 is correct. You can verify this by using the aforesaid online normal distribution calculator. In fact, I would recommend that you do so.