Help ! please help ! can you show work step by step ??? Theoretical distributions and z-scores

YOU MUST show your work !

1. The distribution of 800 test scores in an introduction to psychology course was approximately normal, with = 35, = 10.

a. What proportion of the students had scores between 30 and 40?

b. What is the probability that a randomly selected student would score between 30 and 40?

2. Would you expect to find the same proportion between scores of 20 and 30? Why or why not?

3. Calculate the proportion of scores between 20 and 30. Be careful here: drawing a picture strongly advised.

4. How many of the 800 students would be expected to have scores between 20 and 30?