AST 311 Homework 2 List, page 1 of 1 Problem 1) The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that the weights of all such animals can be described by a normal model with a mean of 1152 pounds as stated, and a standard deviation of 84 pounds. Answer the following based on that model. For parts a through f, your answer should include a sketch of the distribution showing and the area of interest shaded and the calculation itself. a) b) c) d) e) f) g) What proportion of Angus steers weighs more than 1400 pounds? What proportion of Angus steers weighs less than 1202 pounds? What proportion of Angus steers weighs between 887 and 1075 pounds? What is the value for Q1 for the weights? A rancher wants to examine the smallest 20% of his herd. What is the corresponding cutoff weight? A particular buyer wants to purchase the largest 15% of the herd. What is the corresponding cutoff weight? Based on z scores, which would be more unusual, a steer weighing 1000 pounds or one weighing 1250 pounds? No sketch needed. h) Sketch the distribution for the weight of these cattle showing the mean and the weights corresponding to the 68-95-99.7 rule. i) What are the individuals? What is the response variable and its units and type? Problem 2) There are two professors who teach introductory statistics at a certain college: Mr. B and Ms. S. They give similar exams on the first few chapters of the text. The distribution of grades for Mr. B's class is approximately normal with mean 73 and standard deviation 4, while the distribution of grades for Ms. S's class is also approximately normal with mean 81 and standard deviation 9. a) One of Mr. B's students earns 76, while one of Ms. S's students earns 85. Based on z scores, which student has the higher grade? b) What is the grade for Q3 in Ms. S's class? Problem 3) Reports on a student's test score such as the ACT or a child's weight or height usually give the percentile as well as the actual value of the variable. The percentile is just the cumulative proportion stated as a percent: the percent of all values of the variable e that were lower than this one. For example, if a student took a test and the z score was 0.54, then that student would be in the 70.54th percentile. (Look up 0.54 in N table.) The upper arm lengths of males in the United States are approximately normally distributed with mean 39.1 cm and standard deviation 2.3 cm. Larry, a 60-year-old male in the United States, has an upper arm length of 38.4 cm. What is his percentile