"Fractions and percentages take a singular verb inflection when modifying a noncount noun and the plural verb inflection when they modify a plural noun." -- Celce-Murcia & Larsen-Freeman
Example: Sixty-six percent of the students are satisfied with the class.
https://thegrammarexchange.infopop.cc/topic/percentage-is-or...The Oxford Dictionary defines "population" as both countable and uncountable, depending on how you look at it:
population: [countable, uncountable] all the people who live in a particular area, city, or country; the total number of people who live there
https://www.oxfordlearnersdictionaries.com/us/definition/ame...If we consider "population" as noncount, the verb obviously takes the singular (i.e. the population needs). If we consider it countable, it's still a singular noun (i.e. this one particular population versus other populations on planet Earth, maybe beyond); it's a collective, singular noun.
If the term in question were "people", then the verb has to be "need" because "people" is always a plural noun:
https://www.oxfordlearnersdictionaries.com/us/definition/eng...