ttam10

New Member
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

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

TS Contributor
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

New Member
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

Dason

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

ttam10

New Member
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

New Member
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

Member
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

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