# Question bout normal distribution:

1. Feb 18, 2005

### semidevil

so w/ the normal distribution, to find the area between 2 numbers, say $$P(a \leq Z \leq b),$$, I need to split this up into 2:

$$P(-\infty < z \leq b) - P(-\infty < z < a).$$

my question is, why is it not $$P(a < z < +\infty)$$?

2. Feb 18, 2005

### James R

You could do it that way, if you had tables of values for $P(a < z < +\infty)$, but mostly things are tabulated the other way.

Also:

$$P(a < z < +\infty) = 1 - Pr(-\infty < z < a)$$

Last edited: Feb 18, 2005
3. Feb 18, 2005

### semidevil

so i'm getting confused. I have a question regarding storage space and shipment. they are asking what is the probability that the next shipment will be enough, but at the same time, not overflow the storage space.

so basically $$a < z < b$$. so in my problem, it has to be $$1279.5 \leq Z < 1310.5$$

so first, I break it up, and do $$1279.5 < Z < \infty$$.

on the second part, do I do $$-\infty < z < 1310.5$$ or do I do 1279.5 < z < 1310.5 [/tex]

to me, I think the second one is right...but the way the book is doing it, it seems like it is sayingi f I want to know between a and b, I need to -inf < z < b and also -inf < z < a, which doesn't make that much sense....

4. Feb 18, 2005

### Hurkyl

Staff Emeritus
Maybe there's a way to use those two quantities to determine what you want to know.

5. Feb 20, 2005

### James R

Think of the probability as the area under the bell curve. You want the area between a and b. You have the area between negative infinity and a, and between negative infinity and b. So...