Download Statistics Exam 1: Probability and Descriptive Statistics and more Exams Mathematics in PDF only on Docsity! Statistics 150: Introduction to Statistics Exam 1 - Chapter 1, 2, 3, 4 February 23, 2001 Name: ____________________________________ Section 1 Directions: This section contains five computational problems worth a total of 85 points. For each problem, you must present all your work, as well as the final answer, in order to receive full or partial credit. 1. Presented below are the percentages of the workers in a perfume-producing company cross- classified according to the age of the worker and his or her position within the company. Age Secretarial Production Administrative Part-time < 20 1% 2% 0% 2% 20 - 34 8% 33% 0% 7% 35 - 49 3% 36% 1% 1% ≥ 50 0% 3% 3% 0% The following four events have been defined. A: {a person is a teenager} B: {a person is age 35 and over} C: {a person works in production} D: {a person works part-time} (a) Compute P(B). (5 pts.) (b) Compute P(B∩D). (5 pts.) (c) Compute P(D|A). (5 pts.) (d) Are the events A and C independent? Justify your answer. (5 pts.) (e) The number of part-time workers is 53. What is the total number of workers in this company? (4 pts.) Page 1 of 4 2. In a large company that produces stationery items, it is known that 10% of all employees have alcohol-abuse problems and that 7% have drug-abuse problems. The company randomly selected 10 employees to form a committee to address these problems. (a) Compute the standard deviation of the number of alcohol abusers in the committee. (5 pts.) (b) What is the probability that more than two members of the committee are alcohol abusers? (5 pts.) (c) What is the expected number of drug abusers in the committee? (5 pts.) (d) What is the probability that exactly one member of the committee is a drug abuser? (Note: The solution must be manually calculated using the appropriate formula.) (5 pts.) 3. Let X denote the outcome of rolling a fair die. (a) Indicate the sample space using the notation discussed in the textbook and in class. (4 pts.) (b) Verify E(X) = µ = 3.50 using Formula 4.1 in your formula packet. (4 pts.) (c) Compute the variance (σ2) of X using Formula 4.2 in your formula packet. (4 pts.) Page 2 of 4
