This is soo hard i need help please :(

Okay I know how to figure out z scores but I am VERY confused on what kind of answer the teacher is looking for on this following question...

For a normal distribution mean is 100, SD is 8. Use this info to determine area of:

p(x>108) and p(92<x<108)??????? Can anyone help me please??? How am I supposed to do this...

(108 - 100)/8 = 1

(92 - 100)/8 = -1

Where are you wandering off?

I just dont understand the whole area thing?? Is that the answer I have to give for the area??? just the z scores?? THANK YOU FOR YOUR HELP!!

and if the p(x<98) would I switch the signs in my answer bc there is a lesser sign not a greater sign??? Or does that matter??

Sure it matters. It matters what the question is. The z-score, essentially, is just a change of units. Rahter than feet, or degrees, or pounds, you are converting to Standard Deviations.

A mean of 100
A Standard Deviation of 8
108 is 1 Standard Deviation above the mean. By the emperical rule, there is 34% of the total probability in that one standard deviation.
92 is 1 Standard Deviation below the mean. By the emperical rule, there is 34% of the total probability in that one standard deviation.

This enables us to do some arithmetic.

92, being 1 standard deviation below the mean, in addition to 108, 1 standard deviation above the mean, encompasses a total of 68% (34+34) of the total probability.

Okay so that makes since with the 34% per standard deviation..its just adding the different deviations up to get probablity than?? Could it be over 100% by chance?? For example if I had 84 < x< 116 the answer would be 136%???

It's NEVER over 100% - EVER. Go stand in front of a mirror. Say, "The probability is 136%". Then, slap yourself twice.

(84-100)/8 = -16/8 = -2

(116-100)/8 = 16/8 = 2

What does the Empirical Rule tell you about two standard deviations both directions from the mean? 95%

Okay I got that hint! NEVER EVER over 100%! I looked up more on what you wrote out from the empirical stand point and that makes sense. Thank you incredibly much for your help!