Question 335722
a. If she does no preliminary study, how many former students from the pre-med program must she contact to be 90% sure that the point estimate is within 0.1 unit of p?
--
This implies you have no prior knowledge of the "ball park" level of the proportion of students gaining admission. In such cases, you use the conservative value of p=0.5 (because being Binomial in nature, its variance is highest at p=0.5)
--
formula for required sample size is derived from the Margin of Error for a Normal approximation:  {{{ME= Z*Sqrt(p*(1-p)/n)}}} and solving for n
{{{n=Z^2*p*(1-p)/(ME)^2}}}
--
Given 90% confidence and assuming Normal approximation, Z=-\+1.645
{{{n=1.645^2*(0.5*(1-0.5))/0.1^2=67.65}}} since we need whole numbers round up to 68
===

b. A random sample of 36 former students from the pre-med program showed that 24 entered medical school within 6 years from the time they entered the program. How many more must she contact to be 90% sure that the point estimate is within 0.1 unit of p?
--
Having done a preliminary study, you have prior "ball park" knowledge of p.
--
Same as part a) but substitute p=24/36=0.67 instead of p=0.5