1)The chronicle of higher education almanac reports that the percentage of undergraduates in the united states receiving federal financial aid is 45% at public four-year institutions and 52 % at private four-year institutions. The U.S department of education is interested in questioning a random sample of 100 U.S undergraduate students to assess their satisfaction with federal financial aid procedures and policies.
a)a) Explain the difficulties of obtaining the desired random sample.
b)b) Assume the appropriate percentage above applies to your institution . if a random sample of 100 students from your institution were contacted , what is the approximated probability that 50 or more receive financial aid ? less that 25 ?
c)c) What assumptions must be made in order to answer part b using the normal approximation to the binomial ?