please show your work

as a Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. For all questions on this portion of the test, be sure to check conditions where necessary. 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 were accepted and enrolled for the school year. The high school GPA of those incoming freshme Normal distribution with a mean of 4.39 and a standard deviation of 0.586. [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 1 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. as a Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. For all questions on this portion of the test, be sure to check conditions where necessary. 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 were accepted and enrolled for the school year. The high school GPA of those incoming freshme Normal distribution with a mean of 4.39 and a standard deviation of 0.586. [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 1 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