Probability without z-score?

An0n

New Member
#1
Estimate mean of male students on campus. Standard deviation of the heights of young men is about 2.8 inches. Suppose (unknown to you) the mean height of all male students is 70 inches.
a) If you choose one student at random, what is the probability that he is between 69 and 71 inches tall?
b) What is the probability that the mean height of your sample is between 69 and 71 inches?

I'm trying to help someone taking this class now. When I learned it we used z-scores in order to find the percentile but they said they won't be allowed to use a chart on their test...and I have no clue how to solve this without using z-scores unless you use an integral which is beyond that class. Any help would be appreciated.
 

Dason

Ambassador to the humans
#2
They should probably ask their professor. Unless the range of values they're looking for the probability for is a nice integer multiple of the standard deviation you can't really get a good estimate of the probabilities without just memorizing the table which is useless.