Thread: Help, mean of a sample, with standard deviation of raw data, to get probability.

*********** No Help Required! Figured it out. **************
*********** No Help Required! Figured it out. **************
*********** No Help Required! Figured it out. **************
*********** No Help Required! Figured it out. **************
*********** No Help Required! Figured it out. **************
*********** No Help Required! Figured it out. **************







Hi Everyone,

This is my first post asking for help I have just started education again, and due to the long break from math, have come to you for help.

I will soon be doing some work with statistics and have been trying some practice questions but have gotten stuck on one similar to below...

I don't want to post the question I have to answer, as I want to figure it out myself. However, below is an example and my thoughts so far...

The Math

The standard deviation of the length of 1000 pieces of string is 220mm.
The mean length of 85 pieces of string is 4470mm.

I then need to find out the mean of all the blocks with its standard deviation, AND the confidence interval.

My current thoughts

Originally, I figured I could just multiply the mean of the sample by the total of pieces to get the overall mean. However I realized that it would not be 100% accurate.

So then I thought, If I figured out the standard deviation of the sample I could use that somehow. So for the example above I would get the standard deviation of the sample data by dividing the overall standard deviation by the square root of the sample size...

So...

Standard Deviation of Sample = 220/sqrt85

Standard Deviation of Sample = 23.86

Now I have that standard deviation of the sample I am a bit stuck, I don't know where to go from here. I think I would need to use the bell curve...

Correct me if i'm wrong, but, assuming normal distribution

1 standard deviation away from the mean is 68% of the string lengths
2 standard deviations away from the mean is 95% of the string lengths
3 standard deviations away from the mean is 99% of the string lengths


But should I assume normal distribution? is that accurate?

When I figure the overall mean would I calculate the sample mean (4470mm) minus 2 standard deviations (2*23.86) and multiple by the total strings (1000) to get the lowest possibility mean? and similar to get the highest possible mean?


Thanks for any help,
JungleMath

If these are the confidence intervals for the sample...

4470mm ± 23.86mm represents 68% of sample

4470mm ± 47.72mm represents 95% of sample

4470mm ± 71.58mm represents 99% of sample

I assume then that there is a 99% chance that the mean length of the total strings is between 4398.42mm and 4541.58mm.

But is that true for the total number of strings? or is that only true for the sample?

What do I have to do to get a similar answer as above but for the total number of strings?

********** figured it out **************