1. For Spring 2021, MAT 152 Test 1 grades were skewed to the left with a mean of 80.9 and a standard deviation of 11.6. A statistics teacher takes a sample of his 62 students' grades. (A) Calculate the probability the mean of the 62 test grades was at most 79.5. (8pts)

(B) What mean separates the highest 15% of means from the rest of the means? (9pts)

2. The length of a Hollywood feature film is normally distributed with a mean of 119 minutes and a standard deviation of 22 minutes. (A) Twenty Hollywood features are sampled. What is the probability the mean is at most 112 minutes? (8pts)

(B) Twenty Hollywood features are sampled. How many do you expect to last at most 112 minutes? (8pts)

(C) What is the probability that a Hollywood feature is between 112 and 121 minutes long? (8pts)

(D) Hamilton lasts 2 hours and 40 minutes. Is this unusual? Solve with two different methods and you may not mention z-scores, or anything related to them. (16pts) 3. The flight time from Raleigh Durham International Airport (RDU) to Orlando (MCO) is normally distributed with a mean of 104.9 minutes and a standard deviation of 6.1 minutes. (A) Twenty percent of flights will take more than how many minutes? (9pts)

(B) Calculate the probability a flight takes more than 2 hours. (9pts)

(C) Find the probability a flight takes between 100 and 105 minutes. (8pts)

(D) There are 8 flights on a given day from RDU to MCO. What is the mean of the sampling distribution of these flights? Label our answer with correct statistical notation. (4pts)

(E) What is the standard error of the mean of these 8 flights? Label your answer with correct statistical notation. (5pts)

(F) What is the probability the mean time for these 8 flights is at least 100 minutes? (8pts)