According to data released in 2016,69%of students in the united states enroll in college directly after high school graduation. suppose a sample of 242 recent high school graduates is randomly selected. after verifying the conditions for the central limit theorem are met, find the probability that at most 65% enrolled in college directly after high school graduation.

first, verify that the conditions of the central limit theorem are met.

the random and independent condition ( does not hold, holds assuming independent, holds through an exception)

the large samples condition (holds, does not hold)

the big populations condition (can, cannot) reasonably be assumed to hold.

the probability is