I do not know how to do normal probality density function

Assume that the variable under consideration has a density curve. The area under the density curve that lies to the right of 17 is 0.427. What percentage of all possible observations of the variable exceed 17? What percentage of all possible observations are at most 17?

How can we find the average value of a Continuous Function?

please prove that the t-distribution is normalized. I believe this is done by integrating over -infinity to infinity but I got super thrown with that gamma function in there. Thanks!

I can’t figure out formula or answer for bone density

Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of a normal density function with mean equal to 4 and standard deviation of 1. The graphs would:   Have the same height but one would be shifted 4 units to the right.   Have no horizontal displacement but one would be flatter than the other.   Have no horizontal displacement but one would be steeper that the other.

Assume that the variable under consideration has a density curve. The area under the density curve that lies between 19 and 24 is 0.575. What percentage of all possible observations of the variable are either less than 19 or greater than 24?

How do I find an unknown positive normalizing constant, given x is a continuous unknown and the PDF of x?

The area under the density curve that lies to the left of 10 is 0.654. What percentage of all possible observations of the variable are a. less than 10? b. at least 10?

Could you please resolve the maximum likelikhood and expectataion with the above corrected density equation?