Topic 7 - UKEQ1013 Quantitative Techniques I(May 2015...

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UKEQ1013 Quantitative Techniques I (May 2015) 1 UNIVERSITI TUNKU ABDUL RAHMAN FACULTY OF ACCOUNTANCY AND MANAGEMENT ACADEMIC YEAR 2011/2012 TUTORIAL 14 (Questions) Self-Practice Questions 1. The probability distribution for the number of machine A sold daily in a small company as per bellows: Number of Machine A Sold Daily ( X ) P ( X ) 0 0.10 1 0.20 2 0.45 3 0.15 4 0.05 5 0.05 a. Compute the mean or expected number of machine A sold per day. b. Compute the standard deviation. ( Answer: a. 2.00, b. 1.1832 ) 2. Elly's hot dog emporium is famous for its chilidogs. Elly's latest sales indicate that 30% of the customers ordering her chilidogs order it with hot peppers. Suppose 18 customers are selected at random. a. What is the probability that exactly ten customers will ask for hot peppers? b. What is the probability that between two and six people inclusive want hot peppers? c. What is the probability that fifteen or more customers will want hot peppers? ( Answer: a. 0.015, b. 0.708, c. 0.0000 ) 3. A statistic professor finds she receive on average five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. a. What is the probability that on a randomly selected day she will have no messages? b. What is the probability that on a randomly selected day she will have five messages? c. What is the probability that on a randomly selected day she will have two messages? ( Answer: a. 0.0067, b. 0.175, c. 0.084 ) 4. Using historical records, the personnel manager of a plant has determined the probability distribution of X, the number of employees absent per day. It is x 0 1 2 3 4 5 6 7 P(x) 0.005 0.025 0.310 0.340 0.220 0.080 0.019 0.001 Find the following probabilities.
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UKEQ1013 Quantitative Techniques I (May 2015) 2 (i) P( ) 5 2 X (ii) P( ) 5 X (iii) P( ) 4 X 5. A shopping mall estimates the probability distribution of the number of stores mall customers actually enter, as shown in the table. x 0 1 2 3 4 5 6 P(x) 0.04 0.19 0.22 0.28 0.12 0.09 0.06 Find the mean, variance and standard deviation of the number of stores entered. 6. In the town of Hickoryville, an adult citizen has a 1% chance of being selected for jury duty next year. If jury members are selected at random, and the Anderson family includes 5 adults, determine the probability that (i) None of the Andersons will be chosen. (ii) Exactly two of the Andersons will be chosen. (iii) More than 4 of the Andersons will be chosen. (iv) At least 2 of the Andersons will be chosen. 7. The U.S. divorce rate has been reported as 4.2 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed and that x = the number of divorces in this community during the coming year, determine the following: (i) E(x) (ii) P(x = 1) (iii) P(x = 4) (iv) P(x ) 6 (v) P( ) 5 2 X 8. There are 100 computers in a company. The probability of a computer will defect on a certain day is 0.01.
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