minutes. (b) Mr. Jones spends more time traveling than in the library. 6. It is estimated that of the population of England watched last year’s Cup Final on television. If random samples of 100 people are interviewed‚ (a) calculate the mean and variance of the number of people from these samples who watched the Cup Final on television. (b) calculate the probability that more than 30 people watched the Cup Final on television. 7. Four hundred pupils sit a test which consists of 80 true-false
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1. This problem is in reference to students who may or may not take advantage of the opportunities provided in QMB such as homework. Some of the students pass the course‚ and some of them do not pass. Research indicates that 40% of the students do the assigned homework. Of the students who do homework‚ there is an 80% chance they will pass the course. The probability of not passing if the student does not do the home work is 90%. What is the probability of a student not doing homework or
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tossed 100 times. Estimate the probability that the number of heads lies between 40 and 60 using central limit theorem(the word between in mathematics means inclusive of the endpoints). Solution: The expected number of heads is 100 1 = 50‚ and the variance for the number of heads is 2 11 100 2 2 = 25. Thus‚ since n = 100 is reasonably large‚ we have Sn − 50 ∼ N (0‚ 1) 5 40 − 50 60 − 50 ∗ P (40 ≤ Sn ≤ 60) = P ≤ Sn ≤ 5 5 ∗ = P (−2 ≤ Sn ≤ 2) ∗ Sn = = 2[φ(2) − 0.5] = 2 ∗ (.4772) = .9544 Problem 2 An
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were three different methods used to gather information within the study. The Global Estimation model included using a questionnaire-based survey that would rate the value of a route salesman’s job performance. The CREPID procedure had two raters evaluating the salesman’s performance. The cost accounting method used sales records and performance results records to evaluate based on previous sales and delivery. The results of the study showed that the older‚ more experienced route salesmen had more
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Business Statistics I: QM 1 Lecture N otes by Stefan W aner (5th printing: 2003) Department of Mathematics‚ Hofstra University BUSINESS STATISTCS I: QM 001 (5th printing: 2003) LECTURE NOTES BY STEFAN WANER TABLE OF CONTENTS 0. Introduction................................................................................................... 2 1. Describing Data Graphically ...................................................................... 3 2. Measures of Central Tendency
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STATISTIC (1) A study of the number of cars sold looked at the number of cars sold at 500 Dealers The smallest dealer had 11 cars sold and the largest had 154 cars sold. If you were going to create a frequency distribution of the number of cars sold using six classes in your frequency distribution‚ which of the following might be a reasonable first class? (a) 0 to 25
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Study Set for Midterm II‚ Chapters 7 & 8 ESSAY. Write your answer in the space provided or on a separate sheet of paper. 1) The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 golfers played the course today. Find the probability that the average score of the 36 golfers exceeded 71. 2) At a computer manufacturing company‚ the actual size of computer chips is normally distributed with a mean of 1 centimeter
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EG40JQ/12 UNIVERSITY OF ABERDEEN SESSION 2011 – 2012 Degree Examination in EG40JQ SAFETY AND RELIABILITY ENGINEERING Friday 20 January 2012 Notes: (i) (ii) 2.00 p.m. – 5.00 p.m. Candidates ARE permitted to use an approved calculator Data sheets are attached to the paper. Candidates should attempt all FIVE questions. REGULATIONS: (i) You must not have in your possession any material other than that expressly permitted in the rules appropriate to this examination. Where
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Name: ID: Homework 3 Solutions 1. [§6-4] Let X1 ‚ X2 ‚ . . . ‚ X8 be i.i.d. normal random variables with mean µ and standard deviation σ. Define X −µ ‚ T =√ S 2 /n where X is the sample mean and S 2 is the sample variance. (a) Find τ1 such that P(|T | < τ1 ) = .9; and (b) find τ2 such that P(T > τ2 ) = .05. (a) First‚ we notice that T follows a t7 distribution. Since the t distribution is symmetric about 0‚ we have 0.9 = P(|T | < τ1 ) = P(T < τ1 ) − P(T < −τ1 ) = 2P(T < τ1 ) − 1. Thus P(T < τ1
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Answers to Warm-Up Exercises E8-1. Total annual return Answer: ($0 $12‚000 $10‚000) $10‚000 $2‚000 $10‚000 20% Logistics‚ Inc. doubled the annual rate of return predicted by the analyst. The negative net income is irrelevant to the problem. E8-2. Expected return Answer: Analyst 1 2 3 4 Total Probability 0.35 0.05 0.20 0.40 1.00 Return 5% 5% 10% 3% Expected return Weighted Value 1.75% 0.25% 2.0% 1.2% 4.70% E8-3. Comparing the risk of two investments Answer: CV1 0.10 0.15 0.6667 CV2 0.05
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