1. The University of North Carolina Chapel Hill received over 42,000 application for undergraduate admission for the 2019-2020 school year. Of those applicants, only 4,180 w accepted and enrolled for...

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Extracted text: 1. The University of North Carolina Chapel Hill received over 42,000 application for undergraduate admission for the 2019-2020 school year. Of those applicants, only 4,180 w accepted and enrolled for the school year. The high school GPA of those incoming freshmen has a Normal distribution with a mean of 4.39 and a standard deviation of o.586. [Data collected from publicly available reports at oira.unc.edu] A. Calculate the probability that a single randomly selected student has a high school GPA of 4.00 or less. B. A school counselor surveyed an SRS of 50 incoming freshman from that same school year. Calculate the mean and standard deviation of the sampling distribution of for samples of size n=50. Interpret the standard deviation and be sure to check any relevant conditions. C. What is the shape of the distribution described in part b? Justify your answer. D. The counselor in part B obtained a sample mean of 4.0. Calculate the probability that a random sample of 50 students produces a sample mean at or below the counselor's sample mean.