Let's say we wish to investigate the mistakes made when a straightforward task was performed. During lunch, we send a group of students to the cafeteria and ask them to count the people present. Our research reveals that there were 975 pupils tallied on average, with a standard variation of 15. Assume that the counts are distributed normally.

a) What percentage of the counts will lie between 960 and 990?

b) What percentage of the counts will lie below 975?

c) What percentage of the counts will lie below 990?

d) What two value of counts would encompass the middle 50% of the results?