I would like to estimate the ACT scores of enrolled freshman at a particular university.

I know that ACT scores can only be integers 36 or lower and for a particular school school I know that

75% of freshmen have a 33 or lower 25% <= 31 13% <= 29 1% <= 23

What family of distribution is appropriate given the discrete values that max out at 36?

How should I go by about coming up with a reasonable distribution?

(My first question to SO; please be gentle.)

I would like to estimate the percent of freshmen at a particular university who have each possible ACT score.

I know that ACT scores can only be integers 36 or lower and, for a particular school, I know that:

• 75% of freshmen have a 33 or lower
• 25% <= 31
• 13% <= 29
• 1% <= 23

What family of distribution is appropriate given the discrete values that max out at 36?

How should I go about coming up with a reasonable distribution?

(My first question; please be gentle.)