The students in a large statistics course are completing an extra credit project that seeks to demonstrate how sampling distributions work. One hundred students are participating in the project, and they break up into pairs, with each pair surveying a random sample of forty fellow students. Each group must find the proportion of students in their sample who plan to go to graduate school.

a. The mean of the proportions from all fifty samples conducted by the statistics students is .25. Find the standard error of the sampling distribution.

b. One pair of students finds that 16% of students in their sample plan to go to graduate school. They are surprised that their sample proportion is so high. They want to know how likely it is that a randomly selected proportion would fall below their sample proportion. Find this probability and explain what it means.