In what context has this arisen? If it is a home work problem what have you been covering? Do your notes say anything relevant?

I would consider fitting a beta distribution to the given quantiles (though that will still need some side assumptions), but that is not elementary and I will not do it here.

(a triangular distribution is probably easier to handle than the beta - look at the Wikipedia article on the triangular distribution for the cumulatve triangular distribution function.)

CB