# Question

In the past,25% of a college's students lived in the immediate area. In recent years, the college has been trying to attract students from farther afield. A random sample of 400 students revealed that 82 lived in the immediate area. The college has over 10,000 students.
a. Use Excel to calculate the probability of 82 or fewer students out of 400 coming from the immediate area, assuming the percentage of such students is still 25%.
b. What is for this random sample?
c. What is the probability of getting a sample proportion as low as the you calculated in part b if the percentage of students from the immediate area is still 25%? Use the sampling distribution of to answer this question.
d. Why are the probabilities calculated in parts a and c different?
e. Is there evidence that the percentage of college students from the immediate catchment area is lower than in the past?

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