Suppose that the proportion of students who used the Internet as their major resource for school in the past was 66%. A sample of 1000 students was taken and the number of students who used the Internet for their school during the past year was recorded. Let &#55349;&#56413;̂ be the proportion of students surveyed who used the Internet in the past year.

Question

Suppose that the proportion of students who used the Internet as their major resource for school in the past was 66%. A sample of 1000 students was taken and the number of students who used the Internet for their school during the past year was recorded. Let &#55349;&#56413;̂ be the proportion of students surveyed who used the Internet in the past year.
(A) What is the approximate distribution of &#55349;&#56413;̂ ?
(B) What is the probability that the sample proportion &#55349;&#56413;̂ exceeds 68%?
(C) What is the probability that the sample proportion lies between 64% and 68%?