I am not sure how to solve for a probability when N is not given (beginner help).

#1

I am having the most trouble with part "a)" but I am comparing the two answers so if you feel inclined to discuss part "b)" as well, I would certainly appreciate it!

The problem:
"The average annual age of doctors in a certain hospital is 43.0 years old with a standard deviation of 3.0 years. Assume that the variable is normally distributed.
(a) Find the probability that the age of a randomly selected doctor is less than 42.32 years.
(b) Find the probability that the mean age of a sample of 25 randomly selected doctors is less than 42.32 years."

I know that "normal distribution" entails that mean=median=mode which I'm thinking might help me solve for N but I'm still stumped. Thank you!
 
#2
From your question, I think you can take the supplied values as population parameters.

The "part a" is then a straight forward calculation using a Z-score and a table of values from a standard normal distribution.