Answer all questions with explanation

Suppose that a school considers introducing a short break during the fall semester, to make the fall semester less stressful. To assess whether the students would approve, a sample of 1,000 students is taken from the population of all students enrolled at the school in 2021/2022. Each sampled Mizzou student is either in favor of a short break or not in favor of it. Suppose that, unknown to the administration, 75% of all students are in favor of a short break.

a. What is the probability that at most 700 of the 1,000 sampled students approve of a short break?

b. What is the probability that between 700 and 800 of the 1,000 sampled students approve of a short break?

c. What is the standard deviation of the sample proportion of students in favor of a short break?