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=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!
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.
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