Normal Distribution Question

[love777]

I hope that I am posting in the right thread/forum.

I have this math problem and I cannot understand it at all. There is an example but I cannot relate the example to the question. I would greatly appreicately an explanation for dummies on how to do this problem.

In a set of 110 ACT Scores, where the mean is 26 and the standard deviation is 5.39, (a) how many scores are expected to be lower than 20.61 (one standard deviation below the mean)? (b) How many of the 110 scores are expected to be below the 36.78 (two standard deviations above the mean)?


Any help is greatly appreciated!

 

[HallsofIvy]

I hope that I am posting in the right thread/forum.

I have this math problem and I cannot understand it at all. There is an example but I cannot relate the example to the question. I would greatly appreicately an explanation for dummies on how to do this problem.

In a set of 110 ACT Scores, where the mean is 26 and the standard deviation is 5.39, (a) how many scores are expected to be lower than 20.61 (one standard deviation below the mean)? (b) How many of the 110 scores are expected to be below the 36.78 (two standard deviations above the mean)?


Any help is greatly appreciated!

Well, let's start by seeing what you do know! You titled this "Normal Distribution Question". Are you saying you no know what that is? I started to explain how to change from a normal distribution with given mean and standard deviation (\(\displaystyle z=\frac{x- \mu}{\sigma}\)), but you are given that: the first is "one standard deviation above the mean so the standard variable is z=2. The second says "two standard deviations below the mean, so z= -2.

Look up the probabilities, or proportions, in a table of the "Standard Normal Distribution". There is probably one in your textbook but there are many on the internet. A good one is at http://www.mathsisfun.com/data/standard-normal-distribution-table.html

 

[love777]

I have been trying to understand the example that has been given to me.
The link that you gave to me is in my book.

I know standard deviation of 1 is 34.13%
standard deviation of 2 is 13.59%

So I THINK the answer is:


50%+34.13%+13.59%=97.72%
110*97.72%=107 - lower than 20.61
110*2.28%=3 - below the 36.78

 

[HallsofIvy]

I have been trying to understand the example that has been given to me.
The link that you gave to me is in my book.

I know standard deviation of 1 is 34.13%
standard deviation of 2 is 13.59%

??? You aren't looking for the "standard deviation" on either. Was that just a mis-statement?

So I THINK the answer is:


50%+34.13%+13.59%=97.72%
110*97.72%=107 - lower than 20.61
110*2.28%=3 - below the 36.78

Does your table have only z above the mean? Can you distinguish between "above the mean" and "below the mean". Where did you get that "2.28"? Is it just 1- 97.72? Why would "lower than 20.61" have anything to do with "larger than 36.78.

Finally, does your answer make sense to you? You say there are 107 students who score lower than 20.61, but only 3 who scored lower than 36.78?
You seem to be applying formulas without understanding what you are doing.

 

[love777]

I dont understand that is why I am hoping to get some help here? I am wililng to watch a video something, anything as I do believe in 'knowing' what I am doing.

Based on my complete non understanding and my complete guess in interpreting my text (as this is an online class)

This is here based on the graphs that are in my book.
I know standard deviation of 1 is 34.13%
standard deviation of 2 is 13.59%

I dont even understand the problem? I am okay with Math but this particular one I have zero understanding.
The question completely confuses me.

Does your table have only z above the mean? Can you distinguish between "above the mean" and "below the mean". Where did you get that "2.28"? Is it just 1- 97.72? Why would "lower than 20.61" have anything to do with "larger than 36.78.

2.28 is 100-97.72%
I'm not sure what you second question even means.
I THINK the quesiton is asking how many scored below 20.61 and how many scored below 36.78

I am at a loss and i'm hoping that someone here will dumb it down for me and break it down.
I have litterally spent hours just going through the example in my book and trying to apply it to this question and I just cannot understand it.