Thread: Probability notations

I have a 3 part question and I am fairly confident I have the correct final answer. It goes

A region's population is 7,800 and it's per capita income approximately observes a normal distribution with the mean being $12,100 and the standard deviation being $6,050. Suppose $5,500 is the poverty line. What percent of people in the region live under the poverty line?

So I have

Z=X-mean/ std
Z=5500-12100 / 6050 = - 1.09
P(-1.09 < Z < 0) = P(0<Z<1.09)= 0.3621
0.50- 0. 3621 = 0.1379
7800 * 0.1379 = 1075.62

That's what I have. The thing is, since I am wanting to get a good grade on this from my professor, I am worried I have left out some notations maybe? I mean, I think I have the right answer and everything, but have I "shortcutted" anything, is the process from z-score to final answer as simple as 5 lines? I just want everything to be perfect. I found the z-score, then I expressed a probability...did I do the probability expression right? BTW, my normal table in my book is from 0 to Z to the right of the mean. (I have been posting questions sometimes on Yahoo answers, and people ask me where I am getting my probabilities wrong, as if the table in my book is wrong. I don't know how that could be)

Another part of the question asks: How many people in the region earn an income between $10,000 and $16,000?

Z=X-mean / std
Z= 10000-12100 / 6050 = - 0.35
P(-0.35 < Z<0)= P(0<Z<0.35)= 0.1318

Z= 16000-12100 / 6050 = 0.64
(0<Z<0.64) = 0.2389

That is all I have for this part because I am lost. I am guessing I add the two probabilities but part of me says to subtract. Also, did I do correct notations for this part?

PS I am new to this site, is there a limit to how many times I can post? I don't want to wear out my welcome. I just really want to do perfect work but please be honest if I am wearing anyone out!

Originally Posted by peanutbutter

I have a 3 part question and I am fairly confident I have the correct final answer. It goes

A region's population is 7,800 and it's per capita income approximately observes a normal distribution with the mean being $12,100 and the standard deviation being $6,050. Suppose $5,500 is the poverty line. What percent of people in the region live under the poverty line?

So I have

Z=X-mean/ std
Z=5500-12100 / 6050 = - 1.09
P(-1.09 < Z < 0) = P(0<Z<1.09)= 0.3621
0.50- 0. 3621 = 0.1379
7800 * 0.1379 = 1075.62

That's what I have. The thing is, since I am wanting to get a good grade on this from my professor, I am worried I have left out some notations maybe? I mean, I think I have the right answer and everything, but have I "shortcutted" anything, is the process from z-score to final answer as simple as 5 lines? I just want everything to be perfect. I found the z-score, then I expressed a probability...did I do the probability expression right? BTW, my normal table in my book is from 0 to Z to the right of the mean. (I have been posting questions sometimes on Yahoo answers, and people ask me where I am getting my probabilities wrong, as if the table in my book is wrong. I don't know how that could be)

[snip]

The probability is correct.

But you've used it to find the number of people in the region below the poverty line. Wrong.

The question asks for the percent below the poverty line ....

The percent is (0.1379)(100) = 13.79 %

So not only can I not do math but I also cannot read. So embarassing!!!!!! Thank you sir, at least I got part of the question right this time.

Originally Posted by peanutbutter

[snip]

Another part of the question asks: How many people in the region earn an income between $10,000 and $16,000?

Z=X-mean / std
Z= 10000-12100 / 6050 = - 0.35
P(-0.35 < Z<0)= P(0<Z<0.35)= 0.1318

Z= 16000-12100 / 6050 = 0.64
(0<Z<0.64) = 0.2389

That is all I have for this part because I am lost. I am guessing I add the two probabilities but part of me says to subtract. Also, did I do correct notations for this part?
[snip]

You add (a picture would make that clear):

Pr(10,000 < X < 16,000) = Pr(-0.35 < Z < 0.64) = Pr(-0.35 < Z < 0) + Pr(0 < Z < 0.64) = Pr(0 < Z < 0.35) + Pr(0 < Z < 0.64) = .....

You should make it clearer where your answers are coming from by including a line of calculation similar to the one I've given above.

Originally Posted by peanutbutter

[snip]
PS I am new to this site, is there a limit to how many times I can post?
[snip]

It depends .... are you smooth or crunchy

Oh, I see what you mean, I should have a line of calculations from beginning of the probability process to the end result. Instead of those little snippets one right under the other. btw I guess I am crunchy, if I were smooth I wouldn't have so many problems. lol! Ooops then, the last part of the string would be P(0<Z<0.35) + P(0<Z<0.64)= 0.1368 + 0.2389 = 0.3757. Then 0.3757 * 7800= 2930.46. Thanks for helping

Originally Posted by peanutbutter

Oh, I see what you mean, I should have a line of calculations from beginning of the probability process to the end result. Instead of those little snippets one right under the other. btw I guess I am crunchy, if I were smooth I wouldn't have so many problems. lol! Ooops then, the last part of the string would be P(0<Z<0.35) + P(0<Z<0.64)= 0.1368 + 0.2389 = 0.3757. Then 0.3757 * 7800= 2930.46. Thanks for helping

Since you can't have a fraction of a person, you might want to consider rounding ......