normal distribution, probability of occurence of an event between to numbers



I know my question will seem stupid but this is the first time I study statistics so some basic things seem just incredible to me.
My question is related to find a probability when we have a normal distribution, the mean and the standard deviation.

I know we have to calculate z but i don t know how to proceed when the probability we are looking for is for something included between 2 numbers.

lets say I have a mean of 100 and a stdrd deviation of 15 and I want to calculate the probability of something that is included between 110 and 120. how can I do this?

Thank you
firstly, you want to find out p(110<x<120)=? , you should convert into standardized form, it means that p( (110-110)/15<(x- mean) /stdrd deviation<(120-110/15)) then solve , p(0<Z<0.6667) , then see the table Z-table