Gaussian Distribution Question.

[Xyius]

I am studying the Gaussian distribution and am doing one of the problems for practice. The problem states that the standard deviation is equal to 15 and the actual value recorded in the experiment is 385.0. It then asks what is the probability that a single measurement lies in the range of the following..
a.) 385.0-385.1
b.) 400.0-400.1
c.) 451.0-415.1
d.) 370.0-400.0
e.) 355.0-415.0
f.) 340.0-430.0

The following equations are to be used, based on the Gaussian distribution.
[PLAIN]http://img62.imageshack.us/img62/8594/what2c.gif
I couldn't get the same answer as the book. This is the books work for a.)
[PLAIN]http://img585.imageshack.us/img585/1271/whati.gif

There is no explanation as to where 0.399 came from, and the section on Gaussian distribution is very short (As this isn't a statistics course). It says for problems d e and f use the integral equation. Why can't I use the integral equation for all of them? Can anyone help?

 

[Stephen Tashi]

the actual value recorded in the experiment is 385.0.

The problem would make sense if it said that 385.0 was the actual population mean.

There is no explanation as to where 0.399 came from

Taking $z= \frac{(385.1 - 385.0)}{15}$ and substituting this in the expression $\frac{1}{\sqrt{2 \pi} } e^{\frac{-z^2}{2}}$ is probably where it came from. Or they might have used 385.05 as being more representative of the interval from 385 to 385.1 than the endpoint 385.1.

and the section on Gaussian distribution is very short (As this isn't a statistics course). It says for problems d e and f use the integral equation. Why can't I use the integral equation for all of them

I think you could use the integral expression for all of them if you have numerical table of that integral.

 

[Xyius]

Taking $z= \frac{(385.1 - 385.0)}{15}$ and substituting this in the expression $\frac{1}{\sqrt{2 \pi} } e^{\frac{-z^2}{2}}$ is probably where it came from. Or they might have used 385.05 as being more representative of the interval from 385 to 385.1 than the endpoint 385.1.

Yup that was it! But what confuses me is, wouldn't that mean that a and b have the same answer? Since the differences are all 0.1? The book as the the answer to b as, 0.0161.

 

[Stephen Tashi]

The z for a value v is calculated by (v - 385.0)/15. It just happens that in a) the interval begins at 385. In the other examples, the intervals don't begin there.

 

[Xyius]

Ohh! Thank you very much! I understand now :]