Example:

weight of an adult is normally distributed with mean of 180 lbs and std dev of 20 lbs.

1) is the area under the curve equal to 100% or would the area be equal to the mean? The descriptions I see in statistics text books always indicate the probability but wouldn't the integral really be the mean (180 lbs.)?

2) what if I want to know the expected weight of an adult given the weight is above 200 lbs? all the examples I see only talk to what is the probability above or below 200 but I want to know the expected value given that it is above? what area of statistics addresses this question so I can read up on it? is there a formula for a conditional expectation for the normal curve?

Appreciate any help that any stats experts can provide.