Statistics for Economics and Business Assignment 3 Instructions: a. Answer all the questions in numerical order and provide separate answers to each part of a question . All answers must be typewritten in MS Word. . Report your work in detail by showing all the formulas used, however, you can use Excel to check your answers using the formulas. d. Submit your answers to assignment via canvas file upload option e. Failure to follow these instructions will result in loss of points 1. (30 points) Most business schools require that every applicant for admission to a graduate degree program take the GMAT test. Suppose the GMAT scares of all students whao took this test this year have a normal distribution with a mean of M = 550 and a standard deviation of g = 90. a. What is the probability that Anna, a student who took the GMAT this year, will score higher than 6707 b. What is the probability that Chris, a student who took the GMAT this year, will score less than 610? c. What is the GMAT score for which only 10 percent of examines had a score more than this score? Hint: For questions similar to this question, see my notes for chapter 7, pages 1-2 2. (40 points) The International Tennis Federation (ITF) detines the otficial diameter as 2.57-2.70 inches. Suppose the diameter of a brand of tennis balls is approximately normally distributed, with a mean of y = 2.63 inches and a standard deviation of o = 0.03 inch. Suppose we select a random sample of nine tennis balls. a. According to the central limit theorem, what is the sampling distribution of the sample mean (X ) look like? Discuss b. What is the expected value (mean), and standard error of the sample means in part a? Show your work . What is the importance of the Central Limit Theorem in inferential statistics where we draw a conclusion about a population mean based on a random sample of data taken from that population? Discuss d. What are the three desirable properties of an estimator, such as the sample mean? Why are regarded as "desirable\"? Discuss 3. (30 points) Weekly production of backup electricity generators at General Electronics Company (GEC) follows a normal distribution with a mean of K = 4000 units per week and a standard deviation of o = 60 units. Management at GEC is considering adopting a bonus system to increase production. a. One suggestion is to pay a bonus to production workers on the highest 5% of production. What is the minimum production that will qualify a worker for this bonus? Show your work b. Suppose the management would like to give a bonus to production workers on the highest 10% of production. What is the minimum production that will quality a worker for this bonus? Show your work . Suppose the management at GEC would like to identify the top 10% and the bottom 10% of weekly production of backup electricity generators. What are these two production levels? Compute. Hint: For questions similar to question 2, 3, and 4, see my notes for chapter 7